# Existence and regularity of strict critical subsolutions in the stationary ergodic setting

Abstract : We prove that any continuous and convex stationary ergodic Hamiltonian admits critical subsolutions, which are strict outside the random Aubry set. They make up, in addition, a dense subset of all critical subsolutions with respect to a suitable metric. If the Hamiltonian is additionally assumed of Tonelli type, then there exist strict subsolutions of class $\CC^{1,1}$ in $\R^N$. The proofs are based on the use of Lax--Oleinik semigroups and their regularizing properties in the stationary ergodic environment, as well as on a generalized notion of Aubry set.
Type de document :
Pré-publication, Document de travail
2012
Domaine :

https://hal.inria.fr/hal-00724792
Contributeur : Estelle Bouzat <>
Soumis le : mercredi 22 août 2012 - 16:14:57
Dernière modification le : mercredi 27 juillet 2016 - 14:48:48

### Identifiants

• HAL Id : hal-00724792, version 1
• ARXIV : 1205.3351

### Citation

Andrea Davini, Antonio Siconolfi. Existence and regularity of strict critical subsolutions in the stationary ergodic setting. 2012. 〈hal-00724792〉

### Métriques

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