SIAM Review, ISSN 0036-1445, 2017, Volume 59, Issue 4, pp. 703 - 766

.... Proofs of the existence of minimizers usually rely on a fine property of the functional called weak lower semicontinuity...

Quasiconvexity | Null Lagrangians | Weak lower semicontinuity | Calculus of variations | Polyconvexity | MATHEMATICS, APPLIED | CONTINUUM LIMITS | STOCHASTIC HOMOGENIZATION | PHASE-TRANSITIONS | null Lagrangians | quasiconvexity | QUASI-CONVEX INTEGRALS | polyconvexity | NONLINEAR ELASTICITY | calculus of variations | STRONG LOCAL MINIMA | RANK-ONE CONVEXITY | VARIATIONAL-PROBLEMS | A-QUASICONVEXITY | weak lower semicontinuity | Mathematics - Analysis of PDEs

Quasiconvexity | Null Lagrangians | Weak lower semicontinuity | Calculus of variations | Polyconvexity | MATHEMATICS, APPLIED | CONTINUUM LIMITS | STOCHASTIC HOMOGENIZATION | PHASE-TRANSITIONS | null Lagrangians | quasiconvexity | QUASI-CONVEX INTEGRALS | polyconvexity | NONLINEAR ELASTICITY | calculus of variations | STRONG LOCAL MINIMA | RANK-ONE CONVEXITY | VARIATIONAL-PROBLEMS | A-QUASICONVEXITY | weak lower semicontinuity | Mathematics - Analysis of PDEs

Journal Article

Journal of global optimization, ISSN 1573-2916, 2008, Volume 45, Issue 2, pp. 309 - 318

In this paper, the lower semicontinuity and continuity of the solution mapping to a parametric generalized vector equilibrium problem involving set-valued mappings are established by using a new proof...

Scalarization | Lower semicontinuity | Continuity | Solution mappings | Parametric generalized vector equilibrium problems | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | STABILITY | VARIATIONAL INEQUALITY | SOLUTION SET | Studies | Mapping | Optimization

Scalarization | Lower semicontinuity | Continuity | Solution mappings | Parametric generalized vector equilibrium problems | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | STABILITY | VARIATIONAL INEQUALITY | SOLUTION SET | Studies | Mapping | Optimization

Journal Article

ESAIM - Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 04/2015, Volume 21, Issue 2, pp. 513 - 534

We characterize lower semicontinuity of integral functionals with respect to weak...

Quasiconvexity | Free boundary | Lower semicontinuity | MATHEMATICS, APPLIED | free boundary | SEQUENCES | quasiconvexity | RELAXATION | OSCILLATIONS | GRADIENTS | AUTOMATION & CONTROL SYSTEMS | Arches | Integrals

Quasiconvexity | Free boundary | Lower semicontinuity | MATHEMATICS, APPLIED | free boundary | SEQUENCES | quasiconvexity | RELAXATION | OSCILLATIONS | GRADIENTS | AUTOMATION & CONTROL SYSTEMS | Arches | Integrals

Journal Article

Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 12/2015, Volume 22, Issue 6, pp. 1591 - 1605

... DOI 10.1007/s00030-015-0337-y and Applications NoDEA On the lower semicontinuity and approximation of L ∞ -functionals Francesca Prinari Abstract. In this paper...

49A50 | Supremal functionals | Strong Morrey quasiconvexity | 49J45 | Lower semicontinuity | {\Gamma}$$ Γ -convergence | Analysis | Mathematics | Γ-convergence

49A50 | Supremal functionals | Strong Morrey quasiconvexity | 49J45 | Lower semicontinuity | {\Gamma}$$ Γ -convergence | Analysis | Mathematics | Γ-convergence

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 08/2015, Volume 143, Issue 8, pp. 3475 - 3486

Weak supersolutions to the porous medium equation are defined by means of smooth test functions under an integral sign. We show that nonnegative weak...

Porous medium equation | Degenerate diffusion | Lower semicontinuity | Supersolutions | Comparison principle | MATHEMATICS | MATHEMATICS, APPLIED | degenerate diffusion | lower semicontinuity | supersolutions | comparison principle

Porous medium equation | Degenerate diffusion | Lower semicontinuity | Supersolutions | Comparison principle | MATHEMATICS | MATHEMATICS, APPLIED | degenerate diffusion | lower semicontinuity | supersolutions | comparison principle

Journal Article

SIAM journal on mathematical analysis, ISSN 1095-7154, 2018, Volume 50, Issue 1, pp. 779 - 809

.... The functional object of our study is given by a double integral. We establish characterizations of weak lower semicontinuity of the functional in terms of nonlocal versions...

Relaxation | Lower semicontinuity | Peridynamics | Nonlocal variational problems | Young measures | EXISTENCE | MATHEMATICS, APPLIED | VECTOR CALCULUS | lower semicontinuity | relaxation | nonlocal variational problems | WEAK LOWER SEMICONTINUITY | MODEL | MINIMIZERS | peridynamics

Relaxation | Lower semicontinuity | Peridynamics | Nonlocal variational problems | Young measures | EXISTENCE | MATHEMATICS, APPLIED | VECTOR CALCULUS | lower semicontinuity | relaxation | nonlocal variational problems | WEAK LOWER SEMICONTINUITY | MODEL | MINIMIZERS | peridynamics

Journal Article

Advances in calculus of variations, ISSN 1864-8258, 07/2020, Volume 13, Issue 3, pp. 219 - 255

We show general lower semicontinuity and relaxation theorems for linear-growth integral functionals defined on vector measures that satisfy linear PDE side constraints (of arbitrary order...

49J45 | Lower semicontinuity | functional on measures | 35J50 | 74B05 | generalized Young measure | 28B05 | 49Q20 | YOUNG MEASURES | MATHEMATICS | MATHEMATICS, APPLIED | CONVEX | A-quasiconvexity | Integrals | Theorems | Convexity

49J45 | Lower semicontinuity | functional on measures | 35J50 | 74B05 | generalized Young measure | 28B05 | 49Q20 | YOUNG MEASURES | MATHEMATICS | MATHEMATICS, APPLIED | CONVEX | A-quasiconvexity | Integrals | Theorems | Convexity

Journal Article

Operations Research Letters, ISSN 0167-6377, 11/2017, Volume 45, Issue 6, pp. 533 - 537

In this paper, we establish the lower semicontinuity of the solution mapping and the approximate solution mapping for parametric fixed point problems under some suitable conditions...

Parametric fixed point problem | Solution mapping | Lower semicontinuity | Generalized Stackelberg equilibrium problem | Parametric vector quasiequilibrium problem | SOLUTION MAPS | CONTINUITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SET | STABILITY | VECTOR EQUILIBRIUM PROBLEMS

Parametric fixed point problem | Solution mapping | Lower semicontinuity | Generalized Stackelberg equilibrium problem | Parametric vector quasiequilibrium problem | SOLUTION MAPS | CONTINUITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SET | STABILITY | VECTOR EQUILIBRIUM PROBLEMS

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 02/2014, Volume 28, pp. 38 - 41

In this paper, the lower semicontinuity of solution mapping to parametric generalized strong vector equilibrium problems without the assumptions of monotonicity and compactness is established by using...

Parametric generalized strong vector equilibrium problems | Solution mapping | Lower semicontinuity | EXISTENCE | MATHEMATICS, APPLIED | CONTINUITY | STABILITY | INEQUALITY | SOLUTION SET | EFFICIENT SOLUTIONS | Mapping | Vectors (mathematics) | Mathematical analysis | Proving

Parametric generalized strong vector equilibrium problems | Solution mapping | Lower semicontinuity | EXISTENCE | MATHEMATICS, APPLIED | CONTINUITY | STABILITY | INEQUALITY | SOLUTION SET | EFFICIENT SOLUTIONS | Mapping | Vectors (mathematics) | Mathematical analysis | Proving

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2016, Volume 2016, Issue 1, pp. 1 - 14

This paper is mainly concerned with the upper semicontinuity, closedness, and the lower semicontinuity of the set-valued solution mapping for a parametric lexicographic equilibrium problem...

closedness and lower semicontinuity | Analysis | parametric generalized lexicographic quasiequilibrium problem | Mathematics, general | Mathematics | Applications of Mathematics | upper semicontinuity | VARIATIONAL-INEQUALITIES | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | CONTINUITY | STABILITY | OPTIMIZATION | SOLUTION MAPPINGS | Mapping | Maps | Inequalities

closedness and lower semicontinuity | Analysis | parametric generalized lexicographic quasiequilibrium problem | Mathematics, general | Mathematics | Applications of Mathematics | upper semicontinuity | VARIATIONAL-INEQUALITIES | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | CONTINUITY | STABILITY | OPTIMIZATION | SOLUTION MAPPINGS | Mapping | Maps | Inequalities

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2011, Volume 152, Issue 1, pp. 256 - 264

.... Under new assumptions, which are weaker than the assumption of C-strict monotonicity, we provide sufficient conditions for the lower semicontinuity of the solution maps to two classes of parametric...

f -efficient solutions | Lower semicontinuity | Stability | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Parametric weak generalized Ky Fan inequalities | Scalarization | Mathematics | Theory of Computation | Engineering, general | Applications of Mathematics | Optimization | f-efficient solutions | MATHEMATICS, APPLIED | CONTINUITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SET | VECTOR EQUILIBRIUM PROBLEMS | SYSTEMS | EFFICIENT SOLUTIONS | Equality | Studies | Management science | Inequality | International | Maps | Inequalities | Mapping | Topology | Vector spaces

f -efficient solutions | Lower semicontinuity | Stability | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Parametric weak generalized Ky Fan inequalities | Scalarization | Mathematics | Theory of Computation | Engineering, general | Applications of Mathematics | Optimization | f-efficient solutions | MATHEMATICS, APPLIED | CONTINUITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SET | VECTOR EQUILIBRIUM PROBLEMS | SYSTEMS | EFFICIENT SOLUTIONS | Equality | Studies | Management science | Inequality | International | Maps | Inequalities | Mapping | Topology | Vector spaces

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2004, Volume 294, Issue 2, pp. 699 - 711

.... All kinds of semicontinuity are considered: lower semicontinuity, upper semicontinuity, Hausdorff upper semicontinuity and closedness...

Upper semicontinuity | Lower semicontinuity | Quasiequilibrium problems | Closedness of the solution multifunction | Hausdorff upper semicontinuity | Variational inequalities | quasiequilibrium problems | GENERALIZED MONOTONE BIFUNCTIONS | EXISTENCE | MATHEMATICS, APPLIED | SPACES | lower semicontinuity | closedness of the solution multifunction | SENSITIVITY | upper semicontinuity | variational inequalities | VARIATIONAL-INEQUALITIES | MATHEMATICS | MAPPINGS

Upper semicontinuity | Lower semicontinuity | Quasiequilibrium problems | Closedness of the solution multifunction | Hausdorff upper semicontinuity | Variational inequalities | quasiequilibrium problems | GENERALIZED MONOTONE BIFUNCTIONS | EXISTENCE | MATHEMATICS, APPLIED | SPACES | lower semicontinuity | closedness of the solution multifunction | SENSITIVITY | upper semicontinuity | variational inequalities | VARIATIONAL-INEQUALITIES | MATHEMATICS | MAPPINGS

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 1999, Volume 30, Issue 6, pp. 1355 - 1390

...) lower semicontinuity of (u, v) bar right arrow integral(Omega) f(x, u(x), v(x)) dx whenever f : Omega x R-m x R-d...

A-quasiconvexity | Lower semicontinuity | Equi-integrability young measure | equi-integrability | MATHEMATICS, APPLIED | ENERGY | CALCULUS | lower semicontinuity | EQUATIONS | RELAXATION | MINIMIZERS | Young measure | CONVERGENCE | CONSERVATION-LAWS | INTEGRANDS | OSCILLATIONS | GRADIENTS

A-quasiconvexity | Lower semicontinuity | Equi-integrability young measure | equi-integrability | MATHEMATICS, APPLIED | ENERGY | CALCULUS | lower semicontinuity | EQUATIONS | RELAXATION | MINIMIZERS | Young measure | CONVERGENCE | CONSERVATION-LAWS | INTEGRANDS | OSCILLATIONS | GRADIENTS

Journal Article

Bulletin des sciences mathématiques, ISSN 0007-4497, 07/2013, Volume 137, Issue 5, pp. 602 - 616

We isolate a general condition, that we call “localization principle”, on the integrand L:M→[0,∞], assumed to be continuous, under which W1,q-quasiconvexity...

[formula omitted]-quasiconvexity | Localization principle | Young measures | Equi-integrability | Weak lower semicontinuity | quasiconvexity

[formula omitted]-quasiconvexity | Localization principle | Young measures | Equi-integrability | Weak lower semicontinuity | quasiconvexity

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 04/2013, Volume 26, Issue 4, pp. 469 - 472

By using a new assumption, the lower semicontinuity of the efficient solution mappings for parametric vector equilibrium problems without a monotonicity assumption is established...

Efficient solutions | Lower semicontinuity | Parametric vector equilibrium problems | MATHEMATICS, APPLIED | GENERALIZED SYSTEMS | HOLDER CONTINUITY | SOLUTION SETS | STABILITY | INEQUALITY | SOLUTION MAPPINGS

Efficient solutions | Lower semicontinuity | Parametric vector equilibrium problems | MATHEMATICS, APPLIED | GENERALIZED SYSTEMS | HOLDER CONTINUITY | SOLUTION SETS | STABILITY | INEQUALITY | SOLUTION MAPPINGS

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2010, Volume 60, Issue 8, pp. 2417 - 2425

In this paper, the semicontinuities of the solution set map are investigated for a parametric generalized vector quasivariational inequality in locally convex Hausdorff topological vector spaces...

Upper semicontinuity | Hausdorff lower semicontinuity | Parametric gap function | Generalized vector quasivariational inequality | Nonlinear scalarization function | EXISTENCE | MATHEMATICS, APPLIED | INCLUSIONS | THEOREM | STABILITY | OPTIMAL SOLUTION SETS | CONTINUITY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EQUILIBRIUM PROBLEMS | GAP FUNCTIONS | Equality

Upper semicontinuity | Hausdorff lower semicontinuity | Parametric gap function | Generalized vector quasivariational inequality | Nonlinear scalarization function | EXISTENCE | MATHEMATICS, APPLIED | INCLUSIONS | THEOREM | STABILITY | OPTIMAL SOLUTION SETS | CONTINUITY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EQUILIBRIUM PROBLEMS | GAP FUNCTIONS | Equality

Journal Article

Bulletin of the Korean Mathematical Society, ISSN 1015-8634, 2015, Volume 52, Issue 6, pp. 1777 - 1795

In this paper, we establish sufficient conditions for the solution set of parametric generalized vector mixed quasivariational inequality problem to have the semicontinuities such as the...

Lower semicontinuity | Parametric gap function | Inner-openness | H-continuity | Parametric generalized vector mixed quasivariational inequality problem | Hausdorff lower semicontinuity | Continuity | EXISTENCE | SYSTEM | HOLDER CONTINUITY | STABILITY | lower semicontinuity | continuity | parametric gap function | parametric generalized vector mixed quasivariational inequality problem | MATHEMATICS | SENSITIVITY-ANALYSIS | EQUILIBRIUM PROBLEMS | inner-openness | GAP FUNCTIONS

Lower semicontinuity | Parametric gap function | Inner-openness | H-continuity | Parametric generalized vector mixed quasivariational inequality problem | Hausdorff lower semicontinuity | Continuity | EXISTENCE | SYSTEM | HOLDER CONTINUITY | STABILITY | lower semicontinuity | continuity | parametric gap function | parametric generalized vector mixed quasivariational inequality problem | MATHEMATICS | SENSITIVITY-ANALYSIS | EQUILIBRIUM PROBLEMS | inner-openness | GAP FUNCTIONS

Journal Article

18.
Full Text
BV-Ellipticity and Lower Semicontinuity of Surface Energy of Caccioppoli Partitions of ℝ n

The Journal of geometric analysis, ISSN 1559-002X, 2011, Volume 23, Issue 1, pp. 202 - 220

We give a new proof that BV-ellipticity is sufficient for lower semicontinuity of surface energy of Caccioppoli partitions of ℝ n , for any n...

Lower semicontinuity | Caccioppoli partition | Polycrystal | 49Q15 | Mathematics | BV-ellipticity | Abstract Harmonic Analysis | 49J45 | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | EXISTENCE | MATHEMATICS | VARIATIONAL APPROACH | INEQUALITIES | CLUSTERS | SETS | FLOW | FINITE PERIMETER

Lower semicontinuity | Caccioppoli partition | Polycrystal | 49Q15 | Mathematics | BV-ellipticity | Abstract Harmonic Analysis | 49J45 | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | EXISTENCE | MATHEMATICS | VARIATIONAL APPROACH | INEQUALITIES | CLUSTERS | SETS | FLOW | FINITE PERIMETER

Journal Article

Optimization, ISSN 0233-1934, 10/2016, Volume 65, Issue 10, pp. 1781 - 1789

... its domain? We provide a straightforward proof showing that it still holds but only for varying in some interval , where is a quantity expressing quantitatively the violation in the lower semicontinuity of f outside its domain...

Gâteaux differentiability | Ekeland variational principle | lower semicontinuity | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Gateaux differentiability | Optimization

Gâteaux differentiability | Ekeland variational principle | lower semicontinuity | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Gateaux differentiability | Optimization

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 7/2014, Volume 162, Issue 1, pp. 47 - 78

In this paper, two properties of recognized interest in variational analysis, known as Lipschitz lower semicontinuity and calmness, are studied with reference to a general class of variational systems, i.e...

Strict outer slope | Parametric constrained optimization | Mathematics | Theory of Computation | Optimization | Lipschitz lower semicontinuity | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Generalized equation | Implicit multifunction | Applications of Mathematics | Engineering, general | Fréchet subdifferential and coderivative | Calmness | MATHEMATICS, APPLIED | CODERIVATIVE CALCULUS | MULTIFUNCTIONS | Frechet subdifferential and coderivative | STABILITY | SUBREGULARITY | METRIC REGULARITY | CONSTRAINT | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GENERALIZED EQUATIONS | Studies | Analysis | Constraints | Metric space | Mathematical analysis | Stability analysis | Mapping | Derivatives | Recognition

Strict outer slope | Parametric constrained optimization | Mathematics | Theory of Computation | Optimization | Lipschitz lower semicontinuity | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Generalized equation | Implicit multifunction | Applications of Mathematics | Engineering, general | Fréchet subdifferential and coderivative | Calmness | MATHEMATICS, APPLIED | CODERIVATIVE CALCULUS | MULTIFUNCTIONS | Frechet subdifferential and coderivative | STABILITY | SUBREGULARITY | METRIC REGULARITY | CONSTRAINT | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GENERALIZED EQUATIONS | Studies | Analysis | Constraints | Metric space | Mathematical analysis | Stability analysis | Mapping | Derivatives | Recognition

Journal Article

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