Fully nonlinear Hamilton-Jacobi equations of degenerate type

2022/10/27 by Jesús David, Edgard A. Pimentel, Jesus, David +3
Mathematics · #35B65 #35R35 #49L25 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2210.15577

openalex publication_date 2022/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Optimal regularity for degenerate elliptic equations with Hamiltonian terms

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