Lipschitz regularity for censored subdiffusive integro-differential equations with superfractional gradient terms. (January 2016)

• Record Type: Journal Article
• Authors: Barles, Guy; Topp, Erwin
• Is Part Of: Nonlinear analysis. Volume 131(2016)
• Page Start: 3
• Page End: 31
• Publication Date: 2016-01
• Subjects: 35R09 -- 35B51 -- 35B65 -- 35D40 -- 35B10 -- 35B40; Integro-differential equations -- Regularity -- Comparison principles -- Large time behavior -- Strong maximum principles; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.05.013
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: 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.