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a differential variational inequality (DVI) is a dynamical system that incorporates ordinary differential equations and variational inequalities or complementarity
Differential variational inequality
Differential_variational_inequality
Type of mathematical inequality
problem for partial differential equations and coined the name "variational inequality" for all the problems involving inequalities of this kind. Georges
Variational_inequality
dynamical system. Differential variational inequality Dynamical systems theory Ordinary differential equation Variational inequality Differential inclusion Complementarity
Projected_dynamical_system
Differential calculus on function spaces
^ . {\displaystyle y={\hat {y}}.} First variation Isoperimetric inequality Variational principle Variational bicomplex Fermat's principle Principle of
Calculus_of_variations
Concept in Hlibert spaces mathematics
many kinds of inequalities involving matrices and linear operators on Hilbert spaces. This article covers some important operator inequalities connected with
Trace_inequality
Mathematical inequality in Sobolev space theory
the Poincaré inequality is a result in the theory of Sobolev spaces, named after the French mathematician Henri Poincaré. The inequality allows one to
Poincaré_inequality
Theorem in mathematical analysis
through an interpolation inequality. The theorem is of particular importance in the framework of elliptic partial differential equations and was originally
Gagliardo–Nirenberg interpolation inequality
Gagliardo–Nirenberg_interpolation_inequality
{\displaystyle \mathbb {R} ^{d}} . Differential inclusions arise in many situations including differential variational inequalities, projected dynamical systems
Differential_inclusion
Study of rates of change
mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. The primary objects of study in differential calculus
Differential_calculus
Procedure for solving differential equations
mathematics, variation of parameters, also known as variation of constants, is a general method to solve inhomogeneous linear ordinary differential equations
Variation_of_parameters
Differential equation containing derivatives with respect to only one variable
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other
Ordinary differential equation
Ordinary_differential_equation
Canadian-American mathematician (1925–2020)
Gagliardo–Nirenberg interpolation inequality, the Newlander-Nirenberg theorem in complex geometry, and the development of pseudo-differential operators with Joseph
Louis_Nirenberg
Concept in mathematical analysis
and asymptotic behavior for some elliptic variational problems". Calculus of Variations and Partial Differential Equations. 18 (1): 57–75. doi:10.1007/s00526-002-0180-y
Pólya–Szegő_inequality
Quantity defined for a stochastic process
The proof that continuous finite variation processes have zero quadratic variation follows from the following inequality. Here, P {\displaystyle P} is a
Quadratic_variation
Solution with prescribed norm
these problems. For variational problems with prescribed mass, several methods commonly used to deal with unconstrained variational problems are no longer
Normalized solution (mathematics)
Normalized_solution_(mathematics)
Social inequality occurs when resources within a society are unevenly distributed. The differences can be connected with religion, kinship, race, ethnicity
Social_inequality
Branch of mathematics
minimizes the arc length. Many problems in partial differential equations admit a more natural variational characterization, and this can lead to notions
Mathematical_analysis
Differential equation solution with a prescribed norm
these problems. For variational problems with prescribed mass, several methods commonly used to deal with unconstrained variational problems are no longer
Normalized solutions (nonlinear Schrödinger equation)
Normalized_solutions_(nonlinear_Schrödinger_equation)
American mathematician (1943–2024)
solution of the heat equation. These inequalities, known as differential Harnack inequalities or Li–Yau inequalities, are useful since they can be integrated
Richard_S._Hamilton
Distribution of income or wealth between different groups
Economic inequality is an umbrella term for three concepts: income inequality, how the total sum of money paid to people is distributed among them; wealth
Economic_inequality
Slovenian mathematician
degenerate problems (blow-up boundary, singular reactions), inequality problems (variational, hemivariational, both either stationary or evolutionary).
Dušan_Repovš
Young differential equations and makes heavy use of the concept of p-variation. p-variation should be contrasted with the quadratic variation which is
P-variation
Concept in information theory
Inequalities are very important in the study of information theory. There are a number of different contexts in which these inequalities appear. Consider
Inequalities in information theory
Inequalities_in_information_theory
Theorem in analysis
For other inequalities named after Wirtinger, see Wirtinger's inequality. In the mathematical field of analysis, the Wirtinger inequality is an important
Wirtinger's inequality for functions
Wirtinger's_inequality_for_functions
Motivating example in mathematical study
problem is a classic motivating example in the mathematical study of variational inequalities and free boundary problems. The problem is to find the equilibrium
Obstacle_problem
American mathematician (1953–2026)
interpolation inequalities with weights", Compositio Mathematica n. 53 i. 3, pp. 259–275. with Gilbert Strang, "Optimal design and relaxation of variational problems
Robert_V._Kohn
Colombian mathematician (born 1954)
1002/cpa.3160430703 Topics in PDEs̕ and Differential Geometry, Universidade Federal de Goiânia, 2002 Some Variational Problems in Geometry, Instituto Nacional
José_F._Escobar
French mathematician (born 1977)
mechanics. He uses tools from the calculus of variations, nonlinear functional analysis, partial differential equations, and spectral theory. For instance
Mathieu_Lewin
analysis, Croke's proof is based on an inequality of Santaló in integral geometry, while Kleiner adopts a variational approach which reduces the problem to
Cartan–Hadamard_conjecture
Operation in calculus
dx\right)^{1/q}.} For p = q = 2, Hölder's inequality becomes the Cauchy–Schwarz inequality. Minkowski inequality. Suppose that p ≥ 1 is a real number and
Integral
Concept in information theory
Differential entropy (also referred to as continuous entropy) in information theory is a property of absolutely continuous probability distributions which
Differential_entropy
Italian mathematician (1922–1978)
his work on the theory of variational inequalities, the calculus of variation and the theory of elliptic partial differential equations. Stampacchia was
Guido_Stampacchia
Mechanical constraint which prevents penetration between two bodies
dynamics, which models the system with unilateral contacts as variational inequalities. In this method, normal forces generated by the unilateral constraints
Unilateral_contact
Theorem in geometry
mathematics, the Brunn–Minkowski theorem (or Brunn–Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue measures) of
Brunn–Minkowski_theorem
Theorem on eigenvalues and eigenvectors of Hermitian matrices
algebraic proof, based on the variational interpretation of eigenvalues, has been published in Magnus' Matrix Differential Calculus with Applications in
Poincaré_separation_theorem
Measure of inequality of a statistical distribution
dispersion intended to represent the income inequality, the wealth inequality, or the consumption inequality within a nation or a social group. It was developed
Gini_coefficient
Number, approximately 3.14
Wirtinger's inequality is the variational form of the Dirichlet eigenvalue problem in one dimension, the Poincaré inequality is the variational form of the
Pi
American mathematician
calculus of variations, partial differential equations, and geometric analysis, and includes the study of geometric aspects of Sobolev-type inequalities, isoperimetric
Robin_Neumayer
Chinese-American mathematician (born 1949)
Hamilton−Li−Yau inequalities are of great importance in the theory of Ricci flow, where Hamilton proved a matrix differential Harnack inequality for the curvature
Shing-Tung_Yau
Formulation of classical mechanics
thinking along the lines of the variational calculus, but did not publish. These ideas in turn lead to the variational principles of mechanics, of Fermat
Lagrangian_mechanics
Italian-French scientist (1736–1813)
of problems of variational calculus with integral constraints. These works devoted to differential calculus and calculus of variations may be considered
Joseph-Louis_Lagrange
Collection of random variables
1511/2013.101.92. Seneta, E. (1998). "I.J. Bienaymé [1796-1878]: Criticality, Inequality, and Internationalization". International Statistical Review / Revue Internationale
Stochastic_process
French mathematician (born 1956)
number of contributions to the fields of partial differential equations and the calculus of variations. He was a recipient of the 1994 Fields Medal. Lions
Pierre-Louis_Lions
Social equity in health
(2016-07-14). "Unequal representation of genetic variation across ancestry groups creates healthcare inequality in the application of precision medicine". Genome
Health_equity
Italian mathematician (1922–1996)
solution of the Signorini problem and the foundation of the theory of variational inequalities. Fichera's relations with Severi were not as friendly as with Signorini
Gaetano_Fichera
Curve external to a family of curves in geometry
) {\displaystyle u(x;a)} is a solution of the differential equation. A new solution of the differential equation can be constructed by first solving (if
Envelope_(mathematics)
Italian mathematician (1940–2020)
Intern. Congress of Math. 2. 1974. with Antonio Capelo: Variational and quasivariational inequalities. Applications to free boundary problems. Chichester/New
Claudio_Baiocchi
Peruvian mathematician
operators, quasiconvex optimization, and variational analysis, with applications in variational inequality problems and game theory. In 2003, García
Yboon_García_Ramos
Type of differential equation
In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time
Delay_differential_equation
Elastostatics problem in linear elasticity
the Signorini problem coincides with the birth of the field of variational inequalities. The content of this section and the following subsections follows
Signorini_problem
Method for constructing existence proofs and calculating solutions in variational calculus
L 1 ( Ω ) {\displaystyle b\in L^{1}(\Omega )} such that the following inequality holds true for almost every x ∈ Ω {\displaystyle x\in \Omega } and every
Direct method in the calculus of variations
Direct_method_in_the_calculus_of_variations
Mathematics of smooth surfaces
In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most
Differential geometry of surfaces
Differential_geometry_of_surfaces
Theory of economic growth
prosperity. Yet, variations in deeply rooted institutional, cultural, geographical, and human diversity characteristics contributed to the differential timing of
Unified_growth_theory
lemma to an equality. As such, it has been useful for the study of many variational problems. Let (X, μ) be a measure space and let fn be a sequence of measurable
Brezis–Lieb_lemma
Average uncertainty in variable's states
average outcome of a variable is. For a continuous random variable, differential entropy is analogous to entropy. The definition E [ − log p ( X ) ]
Entropy_(information_theory)
American mathematician and Nobel Laureate (1928–2015)
contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations. Nash and fellow game theorists John Harsanyi
John_Forbes_Nash_Jr.
Analyzes the topology of a manifold by studying differentiable functions on that manifold
In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions
Morse_theory
Mathematical way of attaining a desired output from a dynamic system
respectively. Furthermore, it is noted that the path constraints are in general inequality constraints and thus may not be active (i.e., equal to zero) at the optimal
Optimal_control
American mathematician
Mellon University. He works on partial differential equations, minimal surfaces, and variational inequalities, with mathematical applications to the microstructure
David_Kinderlehrer
of inequalities Triangle inequality Bernoulli's inequality Cauchy–Schwarz inequality Hölder's inequality Minkowski inequality Jensen's inequality Chebyshev's
List_of_real_analysis_topics
Italian mathematician (born 1984)
Italian mathematician working primarily on the calculus of variations and partial differential equations. He was awarded the Peccot-Vimont Prize and the
Alessio_Figalli
French mathematician (1928–2001)
Ehrling's lemma Inverse problem Titchmarsh convolution theorem Variational inequality List of second-generation Mathematicians CORE Fields Medal Talk:
Jacques-Louis_Lions
Real function with finite total variation
Variation were introduced by Luigi Ambrosio and Ennio De Giorgi in the paper (Ambrosio & De Giorgi 1988), dealing with free discontinuity variational
Bounded_variation
Riemannian manifold equipped with a differential p-form
mathematical field of differential geometry, a calibrated manifold is a Riemannian manifold (M,g) of dimension n equipped with a differential p-form φ (for some
Calibrated_geometry
Method for solving continuous operator problems (such as differential equations)
family of methods for converting a continuous operator problem, such as a differential equation, commonly in a weak formulation, to a discrete problem by applying
Galerkin_method
Matrix used in complex analysis
Milin, starting from the Lebedev–Milin inequality, succeeded in exponentiating the inequalities to obtain inequalities for the coefficients of the univalent
Grunsky_matrix
Shortest paths on a bounded deformed sphere-like quadric surface
"Zur Theorie der Variations-Rechnung und der Differential-Gleichungen" [The theory of the calculus of variations and of differential equations]. Journal
Geodesics_on_an_ellipsoid
Existence and uniqueness of solutions to initial value problems
In mathematics, specifically the study of differential equations, the Picard–Lindelöf theorem gives a set of sufficient (but not necessary) conditions
Picard–Lindelöf_theorem
Harmonic functions as solutions to Laplace's equation
is the consideration of inequalities they satisfy. Perhaps the most basic such inequality, from which most other inequalities may be derived, is the maximum
Potential_theory
Type of partial differential equation
solutions of the differential equation − ∇ 2 u = f , u | ∂ Ω = g {\displaystyle -\nabla ^{2}u=f,\qquad u|_{\partial \Omega }=g} satisfy a variational principle
Free_boundary_problem
Concept in economics
economics, wage dispersion is the variation in wages encountered in an economy. Search theory Price dispersion Economic inequality Wage ratio Dale T. Mortensen
Wage_dispersion
1960 article by Eugene Wigner
Euclidean than a test of the properties of the gravitational field. The inequality at the heart of the uncertainty principle of quantum mechanics follows
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences
Austrian-American mathematician (1928-2017)
mathematician, known for his contributions to variational methods for eigenvalue problems, partial differential equations, and fluid dynamics. He obtained
Hans_Weinberger
Italian mathematician (1940–2024)
his contributions to the fields of calculus of variations, regularity theory of partial differential equations, minimal surfaces and history of mathematics
Enrico_Giusti
German mathematician (born 1958)
1958) is a German mathematician whose research concerns differential geometry and partial differential equations. He is known for foundational contributions
Gerhard_Huisken
formulated and proved the theorem of the properties of the Poincaré variational equations that states: “If the unperturbed motion of a holonomic potential
Nikolay_Gur'yevich_Chetaev
Open source scientific software for modeling non-smooth dynamical systems
systems, differential inclusions, optimal control with state constraints), Optimization (Complementarity problem and Variational inequality) Biology Gene
Siconos
Italian mathematician (born 1985)
Fiesole) is an Italian mathematician. He works on the calculus of variations, partial differential equations and geometric measure theory. In 2016, he was awarded
Guido_De_Philippis
French-American mathematician (1937–2022)
particular numerical solution and applications of partial differential equations and variational inequalities. He was a member of the French Academy of Sciences
Roland_Glowinski
Concept in labour economics
compensation differential, pay differential, and wage differential (see wage dispersion or economic inequality) are also used in economics, but normally have
Compensating_differential
Theorem about metric spaces
David; Stampacchia, Guido (1980). "Variational Inequalities in RN". An Introduction to Variational Inequalities and Their Applications. New York: Academic
Banach_fixed-point_theorem
Effects of income inequality, researchers have found, include higher rates of health and social problems, and lower rates of social goods, a lower population-wide
Effects of economic inequality
Effects_of_economic_inequality
Technique for solving hyperbolic partial differential equations
parabolic partial differential equations. The method is to reduce a partial differential equation (PDE) to a family of ordinary differential equations (ODEs)
Method_of_characteristics
Romanian mathematician
Nonlinear Differential Equations of Monotone Types in Banach Spaces Convexity and Optimization in Banach Spaces Optimal Control of Variational Inequalities "Pagina
Viorel_P._Barbu
American mathematician
(1961–2025) was an American mathematician specializing in differential geometry and the calculus of variations. He was a professor at ETH Zurich. He obtained his
Tom_Ilmanen
Australian mathematician (born 1945)
Bray, Hubert L. Proof of the Riemannian Penrose inequality using the positive mass theorem. J. Differential Geom. 59 (2001), no. 2, 177–267. Hoffman, David;
Leon_Simon
Type of vector space in math
and partial differential equations, Springer. Buttazzo, Giuseppe; Giaquinta, Mariano; Hildebrandt, Stefan (1998), One-dimensional variational problems,
Hilbert_space
Branch of mathematics concerning probability
methods for ordinary differential equations Numerical methods for partial differential equations Validated numerics Variational calculus Probability theory
Probability_theory
French mathematician
contributed also to elasticity, to the theory of plates and shells and differential geometry. Philippe Ciarlet is a former student of the École Polytechnique
Philippe_G._Ciarlet
Function whose values are sets (mathematics)
optimal control, partly as a generalization of convex analysis; the term "variational analysis" is used by authors such as R. Tyrrell Rockafellar and Roger
Set-valued_function
Italian mathematician
mathematician who is active in the fields of partial differential equations and calculus of variations, with several contributions to geometric analysis
Andrea_Malchiodi
American mathematician (1927-1984)
made fundamental contributions to the calculus of variations and the theory of partial differential equations. Charles Bradfield Morrey Jr. was born July
Charles_B._Morrey_Jr.
Quantum field theory enjoying conformal symmetry
four-point functions obey certain inequalities. Powerful numerical bootstrap methods are based on exploiting these inequalities. A conformal field theory is
Conformal_field_theory
Italian mathematician
his contributions to the fields of calculus of variations, regularity theory of partial differential equations, and the theory of symmetrization. He
Nicola_Fusco
Theorem in functional analysis
the min-max theorem, or variational theorem, or Courant–Fischer–Weyl min-max principle, is a result that gives a variational characterization of eigenvalues
Min-max_theorem
French mathematician (1942–2009)
and was a leading expert on Riemannian geometry and non-linear partial differential equations. His fundamental contributions to the theory of the Yamabe
Thierry_Aubin
ISBN 978-0-02-398415-0. Roubíček, T. (1997). Relaxation in Optimization Theory and Variational Calculus. Berlin: Walter de Gruyter. ISBN 978-3-11-014542-7.
Relaxation_(approximation)
Soviet mathematician
mathematician of Jewish origin known for contributions to partial differential equations, differential geometry, probability theory, and approximation theory. Bernstein
Sergei_Bernstein
Conformal structure admits a Hodge dual of 1-forms without even specifying a metric
harmonic and holomorphic differentials with prescribed singularities. These methods were first used by Hilbert (1909) in his variational approach to the Dirichlet
Differential forms on a Riemann surface
Differential_forms_on_a_Riemann_surface
preserves the symplectic structure Variational integrator — symplectic integrators derived using the underlying variational principle Semi-implicit Euler method
List of numerical analysis topics
List_of_numerical_analysis_topics
DIFFERENTIAL VARIATIONAL-INEQUALITY
DIFFERENTIAL VARIATIONAL-INEQUALITY
Boy/Male
Hindu, Indian
Variation
Girl/Female
Indian, Kannada
Most Highly Adored; Most Praised; Variation of Muhammad
Girl/Female
Christian, Indian, Spanish
Dedicated to God; Variation of Isabel
Boy/Male
Australian, Danish, Dutch, German, Hebrew
Variation of Jenny; Diminutive of Jane and Jennifer
Boy/Male
Hindu
Variation to Shanti meaning peacefulness
Girl/Female
American, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Greek, Irish, Latin
Pearl; Child of Light; Variation of Margaret
Boy/Male
Tamil
Variation to Shanti meaning peacefulness
Girl/Female
American, British, English, French, German
Truthful; Variation of Alice; Noble
Girl/Female
Muslim
Angel, Variation of anaitis
Girl/Female
American, Australian, Greek
Protector of Men; Variation of Sandra or Chandra
Boy/Male
Indian
First; Variation of Pratham
Girl/Female
Indian
Angel, Variation of anaitis
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
A Variation of the Name Sukumaran
Girl/Female
American, Australian, British, Chinese, Christian, English, German, Hebrew, Scandinavian
Doe; Ewe; Wise Protection; Variation of Raymond; Female Sheep
Girl/Female
American, British, English, French
Fair-haired; Variation of the Spanish Blandina; Flattering
Boy/Male
British, English
The Gaelic Harvest Festival; A Variation of Samhain
Boy/Male
Afghan, Arabic, Muslim, Pashtun
One who can Differentiate; Comely; One who Distinguishes Truth from Falsehood
Boy/Male
Hindu, Indian
Variation of Lord Vishnu
Girl/Female
American, Australian, Christian, French, German, Irish
Truthful; Noble; Nobility; Honest; Noble Sort; Variation of Alice
Boy/Male
African, American, Arabic, Bengali, French, Hebrew, Hindu, Indian, Latin, Muslim, Spanish, Tamil
Variation of Adam from the Red Earth; Earth; Man; Heaven
DIFFERENTIAL VARIATIONAL-INEQUALITY
DIFFERENTIAL VARIATIONAL-INEQUALITY
DIFFERENTIAL VARIATIONAL-INEQUALITY
DIFFERENTIAL VARIATIONAL-INEQUALITY
DIFFERENTIAL VARIATIONAL-INEQUALITY
DIFFERENTIAL VARIATIONAL-INEQUALITY
DIFFERENTIAL VARIATIONAL-INEQUALITY
pl.
of Differentia
adv.
Without variation.
n.
An expression which, being differentiated, will produce a given differential. See differential Differential, and Integration. Cf. Fluent.
a.
Of or pertaining to a differential, or to differentials.
n.
The act of varying; a partial change in the form, position, state, or qualities of a thing; modification; alternation; mutation; diversity; deviation; as, a variation of color in different lights; a variation in size; variation of language.
n.
A small difference in rates which competing railroad lines, in establishing a common tariff, allow one of their number to make, in order to get a fair share of the business. The lower rate is called a differential rate. Differentials are also sometimes granted to cities.
n.
A form of conductor used for dividing and distributing the current to a series of electric lamps so as to maintain equal action in all.
n.
A characteristic or essential attribute; a differential.
v. t.
To define or limit by adding a differentia.
adv.
Without variation of termination.
n.
The formal or distinguishing part of the essence of a species; the characteristic attribute of a species; specific difference.
n.
An increment, usually an indefinitely small one, which is given to a variable quantity.
a.
That deduces; inferential.
v. t.
A determining feature; a distinguishing characteristic; a differentia.
v. t.
To distinguish or mark by a specific difference; to effect a difference in, as regards classification; to develop differential characteristics in; to specialize; to desynonymize.
n.
One of two coils of conducting wire so related to one another or to a magnet or armature common to both, that one coil produces polar action contrary to that of the other.
v. t.
To obtain the differential, or differential coefficient, of; as, to differentiate an algebraic expression, or an equation.
a.
Relating to or indicating a difference; creating a difference; discriminating; special; as, differential characteristics; differential duties; a differential rate.
a.
Relating to differences of motion or leverage; producing effects by such differences; said of mechanism.
a.
Ready to obey; reverent; differential; also, servilely submissive.