A general convergence result for viscosity solutions of Hamilton-Jacobi equations and non-linear semigroups

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Abstract

We extend the Barles-Perthame procedure [4] (see also [22]) of semi-relaxed limits of viscosity solutions of Hamilton-Jacobi equations of the type f−λHf=h to the context of non-compact spaces. The convergence result allows for equations on a ‘converging sequence of spaces’ as well as Hamilton-equations written in terms of two equations in terms of operators H and H that serve as natural upper and lower bounds for the ‘true’ operator H. In the process, we establish a strong relation between non-linear pseudo-resolvents and viscosity solutions of Hamilton-Jacobi equations. As a consequence we derive a convergence result for non-linear semigroups.

Original languageEnglish
Article number109346
JournalJournal of Functional Analysis
Volume282
Issue number5
DOIs
Publication statusPublished - 1 Mar 2022

Keywords

  • Barles-Perthame method
  • Hamilton-Jacobi equation
  • Non-linear semigroups
  • Viscosity solutions

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