A condition on the value function both necessary and sufficient for full regularity of minimizers of one-dimensional variational problems

DOI10.1090/S0002-9947-98-01648-1zbMath0888.49028MaRDI QIDQ4382921

Mikhail A. Sychev, Victor J. Mizel

Publication date: 24 March 1998

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

zbMATH Keywords

value functionconditionally equicontinuous familyTonelli partial regularity result

Mathematics Subject Classification ID

Regularity of solutions in optimal control (49N60) Methods involving semicontinuity and convergence; relaxation (49J45) Hamilton-Jacobi theories (49L99)

Related Items (14)

Remarks on necessary conditions for minimizers of one-dimensional variational problems ⋮ Nonoccurrence of the Lavrentiev phenomenon for many nonconvex constrained variational problems ⋮ A necessary and sufficient condition for \(C^1\)-regularity of solutions of one-dimensional variational obstacle problems ⋮ Generic nonoccurrence of the Lavrentiev phenomenon for a class of optimal control problems ⋮ Variational field theory from the point of view of direct methods ⋮ Regularity theory for one-dimensional variational problems with singular ellipticity ⋮ Pathological solutions to the Euler-Lagrange equation and existence/regularity of minimizers in one-dimensional variational problems ⋮ Local minimizers of one-dimensional variational problems and obstacle problems ⋮ Another theorem of classical solvability `in small' for one-dimensional variational problems ⋮ Universal singular sets in the calculus of variations ⋮ Excess action and broken characteristics for Hamilton-Jacobi equations ⋮ Nonoccurrence of gap for infinite-dimensional control problems with nonconvex integrands ⋮ Direct methods in variational field theory ⋮ Nonoccurrence of the Lavrentiev phenomenon for nonconvex variational problems

Cites Work

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• Existence and regularity in the small in the calculus of variations
• One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation
• Singular minimisers in the calculus of variations in one dimension
• Lebesgue measure of the universal singular set for the simplest problems in the calculus of variations
• ON THE QUESTION OF REGULARITY OF THE SOLUTIONS OF VARIATIONAL PROBLEMS

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