Existence and Lipschitz regularity for minima

DOI10.1090/S0002-9939-01-06370-5zbMath0987.49020MaRDI QIDQ2758975

Giulia Treu, Carlo Mariconda

Publication date: 10 December 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Euler equationbarrierLipschitz regularityexistence of minimaLavrentiev

Mathematics Subject Classification ID

Regularity of solutions in optimal control (49N60) Existence theories for free problems in two or more independent variables (49J10)

Related Items (13)

Global continuity of variational solutions weakening the one-sided bounded slope condition ⋮ Hölder continuity of solutions to a basic problem in the calculus of variations ⋮ Unnamed Item ⋮ The bounded slope condition for parabolic equations with time-dependent integrands ⋮ Lipschitz regularity for minima without strict convexity of the Lagrangian ⋮ Parabolic equations and the bounded slope condition ⋮ Lipschitzian continuity of solutions for a problem in the calculus of variations ⋮ Gradient maximum principle for minima ⋮ 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 ⋮ Existence of W^{1,1} solutions to a class of variational problems with linear growth on convex domains

Cites Work

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• Lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands
• Differentiability of minima of non-differentiable functionals
• One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation
• On the equivalence of two variational problems
• Regularity Properties of Solutions to the Basic Problem in the Calculus of Variations
• Multiple Integrals of Lipschitz Functions in the Calculus of Variations
• A comparison principle for minimizers
• On the Bounded Slope Condition and the Validity of the Euler Lagrange Equation
• Gradient maximum principle for minima

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