Boundary continuity of solutions to a basic problem in the calculus of variations

DOI10.1515/ACV.2010.001zbMath1187.49002OpenAlexW1997061110MaRDI QIDQ3400071

Pierre Bousquet

Publication date: 5 February 2010

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/acv.2010.001

zbMATH Keywords

continuitylower bounded slope conditionmultiple integrals calculus of variations

Mathematics Subject Classification ID

Existence theories for optimal control problems involving partial differential equations (49J20) Variational methods for second-order elliptic equations (35J20)

Related Items (13)

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 ⋮ The bounded slope condition for parabolic equations with time-dependent integrands ⋮ Unnamed Item ⋮ Another look to the orthotropic functional in the plane ⋮ Parabolic equations and 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 ⋮ The one-sided bounded slope condition in evolution problems ⋮ Hölder regularity for a classical problem of the calculus of variations ⋮ Lipschitz minimizers for a class of integral functionals under the bounded slope condition

Cites Work

• Growth conditions and regularity. A counterexample
• Lipschitz regularity for minima without strict convexity of the Lagrangian
• Local Lipschitz continuity of solutions to a problem in the calculus of variations
• Regularity for some scalar variational problems under general growth conditions
• Existence and Lipschitz regularity for minima
• LOCAL LIPSCHITZ REGULARITY OF MINIMA FOR A SCALAR PROBLEM OF THE CALCULUS OF VARIATIONS
• Hölder regularity for a classical problem of 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
• Gradient maximum principle for minima

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