Boundary Lipschitz regularity of solutions for general semilinear elliptic equations in divergence form. (October 2022)

• Record Type: Journal Article
• Authors: Liang, Jingqi; Wang, Lihe; Zhou, Chunqin
• Is Part Of: Nonlinear analysis. Volume 223(2022)
• Publication Date: 2022-10
• Subjects: Boundary Lipschitz regularity -- Semilinear elliptic equation -- Dini condition; 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.2022.113026
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study the nonhomogeneous Dirichlet problem concerning general semilinear elliptic equations in divergence form. We establish that the boundary Lipschitz regularity of solutions under some more weaker conditions on the coefficients, the boundary, the boundary function and the nonhomogeneous term. In particular, we assume that the nonhomogeneous term satisfies Dini continuity condition and Lipschitz Newtonian potential condition, which will be the optimal conditions to obtain the boundary Lipschitz regularity of solutions.