Fully nonlinear Hamilton–Jacobi equations of degenerate type. (February 2023) - Jesus, David; Pimentel, Edgard A.; Urbano, José Miguel
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.