A necessary and sufficient condition for -regularity of solutions of one-dimensional variational obstacle problems

  • Jean-Philippe Mandallena

    Université de Nîmes, France
A necessary and sufficient condition for $C^1$-regularity of solutions of one-dimensional variational obstacle problems cover
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Abstract

In this paper we study the -regularity of solutions of one-dimensional variational obstacle problems in when the obstacles are and the Lagrangian is locally Hölder continuous and globally elliptic. In this framework, we prove that the solutions of one-dimensional variational obstacle problems are for all boundary data if and only if the value function is Lipschitz continuous at all boundary data.

Cite this article

Jean-Philippe Mandallena, A necessary and sufficient condition for -regularity of solutions of one-dimensional variational obstacle problems. Rend. Sem. Mat. Univ. Padova 142 (2019), pp. 103–134

DOI 10.4171/RSMUP/33