Approximate convexity principles and applications to PDEs in convex domains. (March 2020)

• Record Type: Journal Article
• Authors: Bucur, Claudia; Squassina, Marco
• Is Part Of: Nonlinear analysis. Volume 192(2020)
• Publication Date: 2020-03
• Subjects: 46E35 -- 28D20 -- 82B10 -- 49A50; Elliptic PDEs -- Convexity -- Concavity -- 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.2019.111661
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We obtain approximate convexity principles for solutions to some classes of nonlinear elliptic partial differential equations in convex domains involving approximately concave nonlinearities. Furthermore, we provide some applications to some meaningful special cases.