Fully nonlinear Hamilton–Jacobi equations of degenerate type. (February 2023)

• Record Type: Journal Article
• Authors: Jesus, David; Pimentel, Edgard A.; Urbano, José Miguel
• Is Part Of: Nonlinear analysis. Volume 227(2023)
• Publication Date: 2023-02
• Subjects: 35B65 -- 49L25 -- 35R35; Degenerate elliptic operators -- Hamilton–Jacobi equation -- Lipschitz regularity -- Two-phase free boundary problems; 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.2022.113181
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We examine Hamilton–Jacobi equations driven by fully nonlinear degenerate elliptic operators in the presence of superlinear Hamiltonians. By exploring the Ishii–Jensen inequality, we prove that viscosity solutions are locally Lipschitz-continuous, with estimates depending on the structural conditions of the problem. We close the paper with an application of our findings to a two-phase free boundary problem.