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Article Dans Une Revue Advances in Calculus of Variation Année : 2018

On the regularity of solutions of one-dimensional variational obstacle problems

Résumé

We study the regularity of solutions of one dimensional variational obstacle problems in $W^{1,1}$ when the Lagrangian is locally H\"older continuous and globally elliptic. In the spirit of the work of Sychev (see [5,6,7]) a direct method is presented for investigating such regularity problems with obstacles. This consists of introducing a general subclass $\mathcal{L}$ of $W^{1,1}$, related in a certain way to one dimensional variational obstacle problems, such that every function of $\mathcal{L}$ has Tonelli's partial regularity, and then to prove that, depending on the regularity of the obstacles, solutions of corresponding variational problems belong to $\mathcal{L}$. As an application of this direct method, we prove that if the obstacles are $C^{1,\sigma}$ then every Sobolev solution has Tonelli's partial regularity.

Dates et versions

hal-01783514 , version 1 (02-05-2018)

Identifiants

Citer

Jean-Philippe Mandallena. On the regularity of solutions of one-dimensional variational obstacle problems. Advances in Calculus of Variation, 2018, 11 (2), pp.203 - 222. ⟨10.1515/acv-2016-0030⟩. ⟨hal-01783514⟩

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