English

Fully nonlinear Hamilton-Jacobi equations of degenerate type

Analysis of PDEs 2022-10-28 v1

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.

Keywords

Cite

@article{arxiv.2210.15577,
  title  = {Fully nonlinear Hamilton-Jacobi equations of degenerate type},
  author = {David Jesus and Edgard A. Pimentel and José Miguel Urbano},
  journal= {arXiv preprint arXiv:2210.15577},
  year   = {2022}
}