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

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• 作者：Andrea Davini ; ^{davini@mat.uniroma1.it" class="auth_mail" title="E-mail the corresponding author} ; Antonio Siconolfi ^{siconolf@mat.uniroma1.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35D40 ; 35B27 ; 35F21 ; 49L25
• 刊名：Annales de l'Institut Henri Poincare (C) Non Linear Analysis
• 出版年：2016
• 出版时间：March-April 2016
• 年：2016
• 卷：33
• 期：2
• 页码：243-272
• 全文大小：532 K

文摘

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${\mathrm{C}}^{1,1}$ in R^N${\mathbb{R}}^N$. 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.