Lipschitz regularity for minima without strict convexity of the Lagrangian

DOI10.1016/j.jde.2007.05.028zbMath1138.49033OpenAlexW2152166272MaRDI QIDQ2464475

Carlo Mariconda, Giulia Treu

Publication date: 21 December 2007

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2007.05.028

zbMATH Keywords

regularityconvexityrelaxationsubdifferentialcalculus of variationsstrictly convexdomainLipschitzLegendreepigraphpolarbounded slope conditionnon-smoothLavrentievdemi-coercivity

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Regularity of solutions in optimal control (49N60) Existence theories for free problems in two or more independent variables (49J10) Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49J30)

Related Items (17)

Global continuity of variational solutions weakening the one-sided bounded slope condition ⋮ An evolutionary Haar-Rado type theorem ⋮ Hölder continuity of solutions to a basic problem in the calculus of variations ⋮ On the Lipschitz Regularity for Minima of Functionals Depending on $x$, $u$, and $\nabla{u}$ under the Bounded Slope Condition ⋮ The bounded slope condition for parabolic equations with time-dependent integrands ⋮ Shape derivatives for minima of integral functionals ⋮ Parabolic equations and the bounded slope condition ⋮ Continuity properties of solutions to some degenerate elliptic equations ⋮ The lack of strict convexity and the validity of the comparison principle for a simple class of minimizers ⋮ LOCAL LIPSCHITZ REGULARITY OF MINIMA FOR A SCALAR PROBLEM OF THE CALCULUS OF VARIATIONS ⋮ On the Lavrentiev phenomenon for multiple integral scalar variational problems ⋮ A Variational Method for Second Order Shape Derivatives ⋮ The one-sided bounded slope condition in evolution problems ⋮ Hölder regularity for a classical problem of the calculus of variations ⋮ Boundary continuity of solutions to a basic problem in the calculus of variations ⋮ Lipschitz minimizers for a class of integral functionals under the bounded slope condition ⋮ A Haar-Rado type theorem for minimizers in Sobolev spaces

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• A relaxation result for autonomous integral functionals with discontinuous non-coercive integrand
• On some regular multiple integral problems in the calculus of variations
• Gradient maximum principle for minima

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