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

Andrea Davini; Antonio Siconolfi

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arXiv · 1205.3351

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

Andrea Davini·Antonio Siconolfi

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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.

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Andrea Davini, Antonio Siconolfi. 2012-05-15. Existence and regularity of strict critical subsolutions in the stationary ergodic setting. https://arxiv.org/abs/1205.3351

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