Fully nonlinear Hamilton–Jacobi equations of degenerate type

David Jesus, Edgard A. Pimentel, José Miguel Urbano*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number113181
JournalNonlinear Analysis, Theory, Methods and Applications
StatePublished - Feb 2023


  • Degenerate elliptic operators
  • Hamilton–Jacobi equation
  • Lipschitz regularity
  • Two-phase free boundary problems

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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