Mixed boundary value problems for fully nonlinear degenerate or singular equations. (October 2022)

• Record Type: Journal Article
• Authors: Birindelli, Isabeau; Demengel, Françoise; Leoni, Fabiana
• Is Part Of: Nonlinear analysis. Volume 223(2022)
• Publication Date: 2022-10
• Subjects: 35J66 -- 35J70 -- 35J75; Mixed boundary conditions -- Fully nonlinear singular or degenerate elliptic equations -- Global holder estimates; 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.2022.113006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove existence, uniqueness and regularity results for mixed boundary value problems associated with fully nonlinear, possibly singular or degenerate elliptic equations. Our main result is a global Hölder estimate for solutions, obtained by means of the comparison principle and the construction of ad hoc barriers. The global Hölder estimate immediately yields a compactness result in the space of solutions, which could be applied in the study of principal eigenvalues and principal eigenfunctions of mixed boundary value problems.