LOCAL LIPSCHITZ REGULARITY OF MINIMA FOR A SCALAR PROBLEM OF THE CALCULUS OF VARIATIONS

DOI10.1142/S0219199708003204zbMath1155.49025MaRDI QIDQ3601331

Giulia Treu, Carlo Mariconda

Publication date: 10 February 2009

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

zbMATH Keywords

strict convexityLipschitz regularitybounded slope conditions

Mathematics Subject Classification ID

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 (15)

Global continuity of variational solutions weakening the one-sided bounded slope condition ⋮ A boundary regularity result for minimizers of variational integrals with nonstandard growth ⋮ An evolutionary Haar-Rado type theorem ⋮ Hölder continuity of solutions to a basic problem in the calculus of variations ⋮ Global Lipschitz continuity for minima of degenerate problems ⋮ On the Lipschitz Regularity for Minima of Functionals Depending on $x$, $u$, and $\nabla{u}$ under the Bounded Slope Condition ⋮ Continuity properties of solutions to some degenerate elliptic equations ⋮ Continuity of solutions of a problem in the calculus of variations ⋮ The lack of strict convexity and the validity of the comparison principle for a simple class of minimizers ⋮ Stable minimizers of functionals of the gradient ⋮ 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

Cites Work

• Unnamed Item
• Lipschitz regularity of the minimizers of autonomous integral functionals with discontinuous non-convex integrands of slow growth
• On the equivalence of two variational problems
• Lipschitz regularity for minima without strict convexity of the Lagrangian
• Local Lipschitz continuity of solutions to a problem in the calculus of variations
• Lipschitzian continuity of solutions for a problem in the calculus of variations
• On the Bounded Slope Condition and the Validity of the Euler Lagrange Equation
• Comparison Results and Estimates on the Gradient without Strict Convexity
• On some regular multiple integral problems in the calculus of variations
• Gradient maximum principle for minima

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