Archive for rational mechanics and analysis, ISSN 1432-0673, 2018, Volume 230, Issue 1, pp. 321 - 342

“It is still not known if the radial cavitating minimizers obtained by Ball (Philos Trans R Soc Lond A 306:557–611, 1982...

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | EXISTENCE | MATHEMATICS, APPLIED | ENERGY | MECHANICS | MAPS | CAVITATION | REGULARITY | DEFORMATIONS | WEAK SOLUTIONS | NONLINEAR ELASTICITY | UNIQUENESS | SURFACES | Cavitation | Deformation | Mathematics - Complex Variables

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | EXISTENCE | MATHEMATICS, APPLIED | ENERGY | MECHANICS | MAPS | CAVITATION | REGULARITY | DEFORMATIONS | WEAK SOLUTIONS | NONLINEAR ELASTICITY | UNIQUENESS | SURFACES | Cavitation | Deformation | Mathematics - Complex Variables

Journal Article

Nonlinear analysis, ISSN 0362-546X, 2015, Volume 120, pp. 186 - 201

In this paper, we introduce and study the notions of Hölder weak sharp minimizers, stable...

Stable Hölder weak sharp minimizer | Hölder tilt-stable minimizer | Hölder metric regularity | Hölder weak sharp minimizer | MATHEMATICS | Holder tilt-stable minimizer | MATHEMATICS, APPLIED | Holder weak sharp minimizer | CALMNESS | SUBREGULARITY | GROWTH | Holder metric regularity | METRIC REGULARITY | OPTIMIZATION | Stable Holder weak sharp minimizer | Nonlinearity | Banach space | Regularity | Optimization

Stable Hölder weak sharp minimizer | Hölder tilt-stable minimizer | Hölder metric regularity | Hölder weak sharp minimizer | MATHEMATICS | Holder tilt-stable minimizer | MATHEMATICS, APPLIED | Holder weak sharp minimizer | CALMNESS | SUBREGULARITY | GROWTH | Holder metric regularity | METRIC REGULARITY | OPTIMIZATION | Stable Holder weak sharp minimizer | Nonlinearity | Banach space | Regularity | Optimization

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Hölder Stable Minimizers, Tilt Stability, and Hölder metric Regularity of Subdifferentials

SIAM journal on optimization, ISSN 1095-7189, 2015, Volume 25, Issue 1, pp. 416 - 438

Using techniques of variational analysis and dual techniques for smooth conjugate functions, for a local minimizer of a proper lower semicontinuous function f on a Banach space, p is an element of (0, +infinity) and q = 1...

Conjugate function | Hölder metric regularity | Hölder tilt-stable minimizer | Hölder stable minimizer | Subdifferential | Holder stable minimizer | Holder tilt-stable minimizer | subdifferential | MATHEMATICS, APPLIED | conjugate function | WEAK SHARP MINIMA | SUBREGULARITY | GROWTH | Holder metric regularity | OPTIMIZATION | ERROR-BOUNDS | Conjugates | Stability | Equivalence | Tilt | Mapping | Banach space | Regularity | Optimization

Conjugate function | Hölder metric regularity | Hölder tilt-stable minimizer | Hölder stable minimizer | Subdifferential | Holder stable minimizer | Holder tilt-stable minimizer | subdifferential | MATHEMATICS, APPLIED | conjugate function | WEAK SHARP MINIMA | SUBREGULARITY | GROWTH | Holder metric regularity | OPTIMIZATION | ERROR-BOUNDS | Conjugates | Stability | Equivalence | Tilt | Mapping | Banach space | Regularity | Optimization

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A hybrid proximal point algorithm for finding minimizers and fixed points in CAT(0) spaces

Journal of Fixed Point Theory and Applications, ISSN 1661-7738, 6/2018, Volume 20, Issue 2, pp. 1 - 19

... of Fixed Point Theory part of Springer Nature 2018 and Applications A hybrid proximal point algorithm for ﬁnding minimizers and ﬁxed points in CA T(0) spaces Godwin...

triangle $$ ▵ convergence | Mathematical Methods in Physics | fixed point | Analysis | demicontractive mapping | 47H09 | CAT space | Mathematics, general | Mathematics | Proximal point | 47J25 | strong convergence | convergence | HILBERT-SPACES | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | Delta convergence | HARMONIC MAPS | METRIC-SPACES | GEODESIC SPACES | STRONG-CONVERGENCE THEOREMS | ITERATIVE ALGORITHMS | WEAK | MATHEMATICS | BANACH-SPACES | MONOTONE-OPERATORS | Algorithms

triangle $$ ▵ convergence | Mathematical Methods in Physics | fixed point | Analysis | demicontractive mapping | 47H09 | CAT space | Mathematics, general | Mathematics | Proximal point | 47J25 | strong convergence | convergence | HILBERT-SPACES | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | Delta convergence | HARMONIC MAPS | METRIC-SPACES | GEODESIC SPACES | STRONG-CONVERGENCE THEOREMS | ITERATIVE ALGORITHMS | WEAK | MATHEMATICS | BANACH-SPACES | MONOTONE-OPERATORS | Algorithms

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Cocompactness and minimizers for inequalities of Hardy–Sobolev type involving N-Laplacian

Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 8/2010, Volume 17, Issue 4, pp. 467 - 477

... Diﬀerential Equations DOI 10.1007/s00030-010-0063-4 and Applications NoDEA Cocompactness and minimizers for inequalities of Hardy–Sobolev type involving N -Laplacian...

Primary 35J20 | Asymptotic orthogonality | 58E05 | 35J60 | Global compactness | Mathematics | Trudinger–Moser inequality | 35J35 | Elliptic problems in two dimensions | Weak convergence | 47J30 | Analysis | Palais–Smale sequences | Secondary 46E35 | Concentration compactness | Trudinger-Moser inequality | Palais-Smale sequences | MATHEMATICS, APPLIED

Primary 35J20 | Asymptotic orthogonality | 58E05 | 35J60 | Global compactness | Mathematics | Trudinger–Moser inequality | 35J35 | Elliptic problems in two dimensions | Weak convergence | 47J30 | Analysis | Palais–Smale sequences | Secondary 46E35 | Concentration compactness | Trudinger-Moser inequality | Palais-Smale sequences | MATHEMATICS, APPLIED

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2012, Volume 389, Issue 2, pp. 915 - 931

.... We will then use it to study cases of equality in the extended Polya-Szegö inequality and discuss applications of such a result to prove the symmetry of minimizers...

Iterated polarization | Weak-strong convergence | Symmetry | MATHEMATICS | INTEGRAL FUNCTIONALS | MATHEMATICS, APPLIED | SYMMETRIZATION | SEQUENCES | LOWER SEMICONTINUITY

Iterated polarization | Weak-strong convergence | Symmetry | MATHEMATICS | INTEGRAL FUNCTIONALS | MATHEMATICS, APPLIED | SYMMETRIZATION | SEQUENCES | LOWER SEMICONTINUITY

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Regularity of Relaxed Minimizers of Quasiconvex Variational Integrals with (p, q)-growth

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 8/2009, Volume 193, Issue 2, pp. 311 - 337

... \rightharpoonup \limits_{k\to\infty}} u\, \rm{weakly\,in}\, W^{1,p}\right\} $$ of F and establish an existence result for minimizers of $${{\fancyscript F}_{\rm loc...

Fluid- and Aerodynamics | Hadamard Condition | Theoretical, Mathematical and Computational Physics | Complex Systems | Classical Mechanics | Partial Regularity | Regularity Result | Weak Lower Semicontinuity | Physics, general | Physics | Weak Minimizer | ELASTICITY | EXISTENCE | GROWTH EXPONENT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CALCULUS | QUASICONVEXITY | LOWER SEMICONTINUITY | RELAXATION | MULTIPLE INTEGRALS | FUNCTIONALS | SINGULAR SET

Fluid- and Aerodynamics | Hadamard Condition | Theoretical, Mathematical and Computational Physics | Complex Systems | Classical Mechanics | Partial Regularity | Regularity Result | Weak Lower Semicontinuity | Physics, general | Physics | Weak Minimizer | ELASTICITY | EXISTENCE | GROWTH EXPONENT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CALCULUS | QUASICONVEXITY | LOWER SEMICONTINUITY | RELAXATION | MULTIPLE INTEGRALS | FUNCTIONALS | SINGULAR SET

Journal Article

ESAIM. Mathematical modelling and numerical analysis, ISSN 1290-3841, 2013, Volume 47, Issue 4, pp. 1077 - 1106

.... the Rogers-McCulloch model. After ensuring the existence of global minimizers, we provide a rigorous proof for the system of first-order necessary optimality conditions...

Bidomain equations | Two-variable ionic models | Weak local minimizer | PDE constrained optimization | MATHEMATICS, APPLIED | pointwise minimum condition | two-variable ionic models | existence theorem | weak local minimizer | necessary optimality conditions | MODEL | bidomain equations

Bidomain equations | Two-variable ionic models | Weak local minimizer | PDE constrained optimization | MATHEMATICS, APPLIED | pointwise minimum condition | two-variable ionic models | existence theorem | weak local minimizer | necessary optimality conditions | MODEL | bidomain equations

Journal Article

St. Petersburg Mathematical Journal, ISSN 1061-0022, 06/2016, Volume 27, Issue 3, pp. 347 - 379

...; some regularity results are proved for related minimizers. These results are the borderline counterpart of analogous ones previously derived for non-autonomous functionals with (p,q)-growth...

Hölder regularity of minimizers | Functionals with nonstandard growth | Holder regularity of minimizers | SMOOTH FUNCTIONS | HOLDER CONTINUITY | LOCAL REGULARITY | RELAXATION | MINIMIZERS | MATHEMATICS | INTEGRAL FUNCTIONALS | SOBOLEV SPACES | LOWER SEMICONTINUITY | ELLIPTIC-EQUATIONS | WEAK SOLUTIONS

Hölder regularity of minimizers | Functionals with nonstandard growth | Holder regularity of minimizers | SMOOTH FUNCTIONS | HOLDER CONTINUITY | LOCAL REGULARITY | RELAXATION | MINIMIZERS | MATHEMATICS | INTEGRAL FUNCTIONALS | SOBOLEV SPACES | LOWER SEMICONTINUITY | ELLIPTIC-EQUATIONS | WEAK SOLUTIONS

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 08/2000, Volume 2, Issue 3, pp. 385 - 404

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 1/2015, Volume 52, Issue 1, pp. 65 - 93

The objective of this paper is to discuss existence, uniqueness and regularity issues of minimizers of one dimensional calculus of variations problem in Hilbert...

Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 49K27 | 49J27 | 49L25 | Mathematics Subject Classification: 49J27, 49K27, 49L25 | MATHEMATICS | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | UNBOUNDED LINEAR TERMS | WEAK KAM THEOREM | DIFFERENTIABILITY | INFINITE DIMENSIONS | HAMILTON-JACOBI EQUATIONS | PRINCIPLE | CONVEX-FUNCTIONS | Hilbert space | Partial differential equations | Mathematical analysis | Regularity | Calculus of variations | Uniqueness

Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 49K27 | 49J27 | 49L25 | Mathematics Subject Classification: 49J27, 49K27, 49L25 | MATHEMATICS | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | UNBOUNDED LINEAR TERMS | WEAK KAM THEOREM | DIFFERENTIABILITY | INFINITE DIMENSIONS | HAMILTON-JACOBI EQUATIONS | PRINCIPLE | CONVEX-FUNCTIONS | Hilbert space | Partial differential equations | Mathematical analysis | Regularity | Calculus of variations | Uniqueness

Journal Article

Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, 03/2014, Volume 156, Issue 2, pp. 209 - 227

.... More precisely, we call a free time minimizer a curve which satisfies the least action principle between any pair of its points without the constraint of time for the variations...

MATHEMATICS | WEAK KAM SOLUTIONS | PARABOLIC TRAJECTORIES | GRAVITATIONAL SYSTEMS | LAGRANGIAN SYSTEMS | Mechanics | Mathematical models | Intervals | Theorems | Dynamic tests | Dynamic mechanical properties | Dynamics | Mathematical analysis | Minimization | Optimization

MATHEMATICS | WEAK KAM SOLUTIONS | PARABOLIC TRAJECTORIES | GRAVITATIONAL SYSTEMS | LAGRANGIAN SYSTEMS | Mechanics | Mathematical models | Intervals | Theorems | Dynamic tests | Dynamic mechanical properties | Dynamics | Mathematical analysis | Minimization | Optimization

Journal Article

JOURNAL OF DIFFERENTIAL EQUATIONS, ISSN 0022-0396, 09/2017, Volume 263, Issue 5, pp. 3090 - 3109

We consider omega-minimizers of functionals with p-growth, and prove higher integrability of the gradient of omega-minimizers by obtaining Calderon-Zygmund type estimates under a sharp condition on omega (center dot...

omega-minimizer | MATHEMATICS | Calderon-Zymgund estimate | Quasi-minimiwsr | MINIMA | REGULARITY | SYSTEMS | ELLIPTIC-EQUATIONS | WEAK SOLUTIONS | GRADIENT | FUNCTIONALS | SINGULAR SET

omega-minimizer | MATHEMATICS | Calderon-Zymgund estimate | Quasi-minimiwsr | MINIMA | REGULARITY | SYSTEMS | ELLIPTIC-EQUATIONS | WEAK SOLUTIONS | GRADIENT | FUNCTIONALS | SINGULAR SET

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The Convergence of Regularized Minimizers for Cavitation Problems in Nonlinear Elasticity

SIAM journal on applied mathematics, ISSN 1095-712X, 2006, Volume 66, Issue 3, pp. 736 - 757

...SIAM J. APPL. MATH. c Vol. 66, No. 3, pp. 736757 THE CONVERGENCE OF REGULARIZED MINIMIZERS FOR CAVITATION PROBLEMS IN NONLINEAR ELASTICITY JEYABAL...

Boundary value problems | Deformation | Mathematical discontinuity | Maps | Boundary conditions | Cavitation flow | Null set | Surface energy | Jacobians | Perceptron convergence procedure | Singular minimizers | Elastic | Weak limit | Regular minimizers | Cavitation | Equilibrium | Convergence | EXISTENCE | regular minimizers | MATHEMATICS, APPLIED | ENERGY | convergence | surface energy | singular minimizers | DEFORMATIONS | GROWTH | elastic | DISTRIBUTIONAL DETERMINANT | equilibrium | weak limit | cavitation

Boundary value problems | Deformation | Mathematical discontinuity | Maps | Boundary conditions | Cavitation flow | Null set | Surface energy | Jacobians | Perceptron convergence procedure | Singular minimizers | Elastic | Weak limit | Regular minimizers | Cavitation | Equilibrium | Convergence | EXISTENCE | regular minimizers | MATHEMATICS, APPLIED | ENERGY | convergence | surface energy | singular minimizers | DEFORMATIONS | GROWTH | elastic | DISTRIBUTIONAL DETERMINANT | equilibrium | weak limit | cavitation

Journal Article

Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 10/2010, Volume 17, Issue 5, pp. 619 - 637

The local boundedness of local quasi-minimizers of integral functionals with variable exponent anisotropic $${\overrightarrow{p}(x...

Weak solution | 49N60 | Analysis | 35J70 | Quasi-minimizer | Boundedness | Anisotropic | Mathematics | Variable exponent | EIGENVALUE | EXISTENCE | MATHEMATICS, APPLIED | REGULARITY | NONSTANDARD GROWTH | ELLIPTIC-EQUATIONS | Anisotropy

Weak solution | 49N60 | Analysis | 35J70 | Quasi-minimizer | Boundedness | Anisotropic | Mathematics | Variable exponent | EIGENVALUE | EXISTENCE | MATHEMATICS, APPLIED | REGULARITY | NONSTANDARD GROWTH | ELLIPTIC-EQUATIONS | Anisotropy

Journal Article

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

We study nonlocal variational problems in L-p, like those that appear in peridynamics. The functional object of our study is given by a double integral. We...

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

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2001, Volume 253, Issue 2, pp. 640 - 650

We prove the existence of second weak derivatives for bounded minimizers u: Ω⊂Rn→RN of the integral ∫Ω(|Du|2+|Dnu|q)dx, when 2

MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | CALCULUS | LOCAL BOUNDEDNESS | SYSTEMS | NONSTANDARD GROWTH | ELLIPTIC-EQUATIONS | WEAK SOLUTIONS | FUNCTIONALS | GROWTH-CONDITIONS | Anisotropy

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 04/2015, Volume 258, Issue 7, pp. 2471 - 2494

For a class of subelliptic p-harmonic systems with the subcritical growth defined in Carnot groups, we prove that the weak solutions belong to...

Morrey's space | Maximum principle | p-harmonic system | Weak solution | Interior regularity | Interior Hölder continuity | P-harmonic system | Interior hölder continuity | LOCAL REGULARITY | EQUATIONS | MINIMIZERS | MATHEMATICS | HEISENBERG-GROUP | Interior Holder continuity | MAPS | Money's space | FUNCTIONALS

Morrey's space | Maximum principle | p-harmonic system | Weak solution | Interior regularity | Interior Hölder continuity | P-harmonic system | Interior hölder continuity | LOCAL REGULARITY | EQUATIONS | MINIMIZERS | MATHEMATICS | HEISENBERG-GROUP | Interior Holder continuity | MAPS | Money's space | FUNCTIONALS

Journal Article

ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, ISSN 0232-2064, 2019, Volume 38, Issue 2, pp. 191 - 208

We prove partial regularity of solutions u of the Dirichlet problem for the nonlinear superelliptic system div A(x, u, Du) + B(x, u, Du) = 0, under natural...

MATHEMATICS, APPLIED | boundary regularity | INTERIOR PARTIAL REGULARITY | Partial regularity | nonlinear system | BOUNDARY-REGULARITY | MINIMIZERS | INTEGRALS | MATHEMATICS | weak solution | Dirichlet problem | subquadratic growth | ELLIPTIC-SYSTEMS | ellipticity

MATHEMATICS, APPLIED | boundary regularity | INTERIOR PARTIAL REGULARITY | Partial regularity | nonlinear system | BOUNDARY-REGULARITY | MINIMIZERS | INTEGRALS | MATHEMATICS | weak solution | Dirichlet problem | subquadratic growth | ELLIPTIC-SYSTEMS | ellipticity

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2006, Volume 221, Issue 2, pp. 412 - 443

We prove local Lipschitz-continuity and, as a consequence, C k and C ∞ regularity of weak solutions u for a class of nonlinear elliptic differential systems of...

Calculus of variations | Regularity | Elliptic differential systems | INTEGRALS | MATHEMATICS | elliptic differential systems | calculus of variations | EQUATIONS | regularity | WEAK SOLUTIONS | MINIMIZERS | PARTIAL REGULARITY

Calculus of variations | Regularity | Elliptic differential systems | INTEGRALS | MATHEMATICS | elliptic differential systems | calculus of variations | EQUATIONS | regularity | WEAK SOLUTIONS | MINIMIZERS | PARTIAL REGULARITY

Journal Article

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