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 C^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.
|Titolo:||Existence and regularity of strict critical subsolutions in the stationary ergodic setting|
|Data di pubblicazione:||2016|
|Citazione:||Existence and regularity of strict critical subsolutions in the stationary ergodic setting / Davini, Andrea; Siconolfi, Antonio. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 33:2(2016), pp. 243-272.|
|Appare nella tipologia:||01a Articolo in rivista|