A necessary and sufficient condition for \(C^1\)-regularity of solutions of one-dimensional variational obstacle problems

DOI10.4171/RSMUP/33zbMath1439.49002OpenAlexW2952101721MaRDI QIDQ2177981

Jean-Philippe Mandallena

Publication date: 7 May 2020

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/rsmup/33

zbMATH Keywords

value function\(C^1\)-regularityone-dimensional variational obstacle problemsconditional equa-continuity

Mathematics Subject Classification ID

Regularity of solutions in optimal control (49N60) Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49J30) Existence theories for free problems in one independent variable (49J05) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

Cites Work

• Interpretation of the Lavrentiev phenomenon by relaxation
• On the regularity of solutions of one-dimensional variational obstacle problems
• Lebesgue measure of the universal singular set for the simplest problems in the calculus of variations
• A condition on the value function both necessary and sufficient for full regularity of minimizers of one-dimensional variational problems
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