Semilinear Dirichlet problem for the fractional Laplacian. (April 2020)

• Record Type: Journal Article
• Authors: Bogdan, Krzysztof; Jarohs, Sven; Kania, Edyta
• Is Part Of: Nonlinear analysis. Volume 193(2020)
• Publication Date: 2020-04
• Subjects: primary 31C05 35R11 -- secondary 60J35 60G22; Fractional Laplacian -- Nonlinear differential equations -- Lipschitz sets; 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.2019.04.011
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We give a general framework and results on existence, representation, and uniqueness of solutions to the semilinear problem for the fractional Laplacian with Dirichlet conditions on the complement and at the boundary of general open sets.