Lipschitz regularity for censored subdiffusive integro-differential equations with superfractional gradient terms

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• 作者：Guy Barles^a ; ^{Guy.Barles@lmpt.univ-tours.fr" class="auth_mail" title="E-mail the corresponding author} ; Erwin Topp^b ; ^{erwin.topp@usm.cl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35R09 ; 35B51 ; 35B65 ; 35D40 ; 35B10 ; 35B40
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：131
• 期：Complete
• 页码：3-31
• 全文大小：776 K

文摘

In this paper we are interested in integro-differential elliptic and parabolic equations involving nonlocal operators with order less than one, and a gradient term whose coercivity growth makes it the leading term in the equation. We obtain Lipschitz regularity results for the associated stationary Dirichlet problem in the case when the nonlocality of the operator is confined to the domain, feature which is known in the literature as censored nonlocality. As an application of this result, we obtain strong comparison principles which allow us to prove the well-posedness of both the stationary and evolution problems, and steady/ergodic large time behavior for the associated evolution problem.