Pathological solutions to the Euler-Lagrange equation and existence/regularity of minimizers in one-dimensional variational problems

DOI10.1016/J.CRMA.2017.01.020zbMath1361.49016OpenAlexW2586360044MaRDI QIDQ517510

Aidys Sedipkov, Richard Gratwick, Aris S. Tersenov, Mikhail A. Sychev

Publication date: 23 March 2017

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.2017.01.020

zbMATH Keywords

Euler equationLavrentiev phenomenonpathological solution

Mathematics Subject Classification ID

Regularity of solutions in optimal control (49N60) Existence of solutions for minimax problems (49J35) Methods involving semicontinuity and convergence; relaxation (49J45) Existence theories for free problems in one independent variable (49J05)

Related Items (2)

Variational field theory from the point of view of direct methods ⋮ Direct methods in variational field theory

Cites Work

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• Another theorem of classical solvability `in small' for one-dimensional variational problems
• One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation
• Singular minimisers in the calculus of variations in one dimension
• Examples of classically unsolvable scalar regular variational problems satisfying standard growth conditions
• On the conditions under which the Euler equation or the maximum principle hold
• Regularity Properties of Solutions to the Basic Problem in 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
• Singular sets and the Lavrentiev phenomenon

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