Nonoccurrence of the Lavrentiev phenomenon for nonconvex variational problems

DOI10.1016/j.anihpc.2004.10.004zbMath1098.49008OpenAlexW1964789705MaRDI QIDQ2575849

Zaslavski, Alexander J.

Publication date: 7 December 2005

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_2005__22_5_579_0

zbMATH Keywords

Lavrentiev phenomenonBanach-valued functionsapproximation in energy

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Existence theories for problems in abstract spaces (49J27) Existence theories for free problems in one independent variable (49J05)

Related Items (6)

On the Euler-Lagrange equation in calculus of variations ⋮ Generic nonoccurrence of the Lavrentiev phenomenon for a class of optimal control problems ⋮ Non-occurrence of gap for one-dimensional non-autonomous functionals ⋮ Equi-Lipschitz minimizing trajectories for non coercive, discontinuous, non convex Bolza controlled-linear optimal control problems ⋮ Property (D) and the Lavrentiev phenomenon ⋮ Nonoccurrence of gap for infinite-dimensional control problems with nonconvex integrands

Cites Work

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• One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation
• A note on approximation of optimal solutions of free problems of the calculus of variations
• Singular minimizers for regular one-dimensional problems in the calculus of variations
• Regularity Properties of Solutions to the Basic Problem in the Calculus of Variations
• On The Lavrentiev Phenomenon
• A condition on the value function both necessary and sufficient for full regularity of minimizers of one-dimensional variational problems

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