Convexity criteria and uniqueness of absolutely minimizing functions

DOI10.1007/s00205-010-0348-0zbMath1223.49002arXiv1003.3171OpenAlexW3098762903MaRDI QIDQ717471

Vesa Julin, Michael G. Crandall, Charles K. Smart, Scott N. Armstrong

Publication date: 4 October 2011

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.3171

zbMATH Keywords

absolutely minimizing propertiescalculus of variations in \(L^\infty\)convexity criteriaequivalences between comparison with cones

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Regularity of solutions in optimal control (49N60) Existence theories for free problems in two or more independent variables (49J10)

Related Items (14)

A Quantitative Sobolev Regularity for Absolute Minimizers Involving Hamiltonian $H({p})$ in Plane ⋮ A Rademacher type theorem for Hamiltonians \(H(x, p)\) and an application to absolute minimizers ⋮ Comparison principles for second-order elliptic/parabolic equations with discontinuities in the gradient compatible with Finsler norms ⋮ Stochastic homogenization of \(L^\infty\) variational problems ⋮ \(L ^{\infty }\) variational problems with running costs and constraints ⋮ \(L^{\infty }\) variational problems for maps and the Aronsson PDE system ⋮ Existence, uniqueness and structure of second order absolute minimisers ⋮ On the numerical approximation of vectorial absolute minimisers in \(L^\infty\) ⋮ Everywhere differentiability of absolute minimizers for locally strongly convex Hamiltonian \(H(p) \in C^{1, 1}(\mathbb{R}^n)\) with \(n \geq 3\) ⋮ Regularity of absolute minimizers for continuous convex Hamiltonians ⋮ Everywhere differentiability of viscosity solutions to a class of Aronsson's equations ⋮ Uniqueness of absolute minimizers for \(L^\infty\)-functionals involving Hamiltonians \(H(x,p)\) ⋮ Vectorial variational principles in \(L^\infty\) and their characterisation through PDE systems ⋮ Nonuniqueness in vector-valued calculus of variations in \(L^\infty\) and some linear elliptic systems

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