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Article Dans Une Revue Rendiconti del Seminario Matematico della Università di Padova Année : 2019

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

Résumé

In this paper we study the $C^1$-regularity of solutions of one-dimensional variational obstacle problems in $W^{1,1}$ when the obstacles are $C^{1,\sigma}$ and the Lagrangian is locally H\"older continuous and globally elliptic. In this framework, we prove that the solutions of one-dimensional variational obstacle problems are $C^1$ for all boundary data if and only if the value function is Lipschitz continuous at all boundary data.
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Dates et versions

hal-02387480 , version 1 (29-11-2019)

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Jean-Philippe Mandallena. A necessary and sufficient condition for $C^1$-regularity of solutions of one-dimensional variational obstacle problems. Rendiconti del Seminario Matematico della Università di Padova, 2019, 142, pp.103-134. ⟨10.4171/RSMUP/33⟩. ⟨hal-02387480⟩

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