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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.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-00724792
Contributor : Estelle Bouzat <>
Submitted on : Wednesday, August 22, 2012 - 4:14:57 PM
Last modification on : Wednesday, July 27, 2016 - 2:48:48 PM

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

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

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