Local minimizers of one-dimensional variational problems and obstacle problems

DOI10.1016/j.crma.2008.07.023zbMath1151.49002OpenAlexW2019842694MaRDI QIDQ957577

Mikhail A. Sychev

Publication date: 28 November 2008

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2008.07.023

zbMATH Keywords

local minimizersSobolev solutionsgeneral existence and regularityone-dimensional variational problemsweak local minimizers

Mathematics Subject Classification ID

Regularity of solutions in optimal control (49N60) Existence theories for optimal control problems involving ordinary differential equations (49J15)

Related Items (1)

Another theorem of classical solvability `in small' for one-dimensional variational problems

Cites Work

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• One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation
• Remarks on necessary conditions for minimizers of one-dimensional variational problems
• Examples of classically unsolvable scalar regular variational problems satisfying standard growth conditions
• Strong versus weak local minimizers for the perturbed Dirichlet functional
• Sufficiency theorems for local minimizers of the multiple integrals of the calculus of variations
• ON THE QUESTION OF REGULARITY OF THE SOLUTIONS OF VARIATIONAL PROBLEMS
• A condition on the value function both necessary and sufficient for full regularity of minimizers of one-dimensional variational problems

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