On some nonlocal problems in the calculus of variations. (April 2022)

• Record Type: Journal Article
• Authors: Chipot, Michel; Mikayelyan, Hayk
• Is Part Of: Nonlinear analysis. Volume 217(2022)
• Publication Date: 2022-04
• Subjects: 35B50 -- 35B51 -- 35J20 -- 49XX -- 49J40; Nonlocal calculus of variations -- Optimization problems -- Obstacle problem -- Variational inequalities -- Penalization; 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.2021.112754
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The goal of this paper is to investigate some nonlocal problems of the calculus of variations where pointwise comparisons principles fail but where some kind of nonlocal maximum principle or monotonicity property remains true for some quantities attached to the problem. A special attention will be given to a nonlocal energy recently introduced in Mikayelyan (2018).