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

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.

Original languageEnglish (US)
Article number113181
JournalNonlinear Analysis, Theory, Methods and Applications
Volume227
DOIs
StatePublished - Feb 2023

Bibliographical note

Funding Information:
EP partially supported by the Centre for Mathematics of the University of Coimbra ( UIDB/00324/2020 , funded by the Portuguese Government through FCT/MCTES ) and by FAPERJ (grants E26/200.002/2018 and E26/201.390/2021 ).

Funding Information:
JMU partially supported by the King Abdullah University of Science and Technology (KAUST), Saudi Arabia , by Fundação para a Ciência e a Tecnologia , through project PTDC/MAT-PUR/28686/2017 , and by the Centre for Mathematics of the University of Coimbra ( UIDB/00324/2020 , funded by the Portuguese Government through FCT/MCTES ).

Funding Information:
DJ was supported by Fundação para a Ciência e a Tecnologia, Portugal , through scholarship PD/BD/150354/2019 , under POCH funds, co-financed by the European Social Fund and Portuguese National Funds from MCTES, and by the Centre for Mathematics of the University of Coimbra, Portugal ( UIDB/00324/2020 , funded by the Portuguese Government through FCT/MCTES ).

Publisher Copyright:
© 2022 Elsevier Ltd

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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