Entropy penalization methods for Hamilton-Jacobi equations

Diogo Gomes, Enrico Valdinoci*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

In this paper we present a new entropy penalization problem and we discuss its relations with approximate solutions of Hamilton-Jacobi equations, the convergence of associated discrete schemes, as well as several applications, such as: a generalization of the Hopf-Cole transformation which converts non-linear Hamilton-Jacobi equations into linear evolution equations, the study of fixed point problems, approximation of certain linear evolution equations, and the construction of entropy penalized Mather measures.

Original languageEnglish (US)
Pages (from-to)94-152
Number of pages59
JournalAdvances in Mathematics
Volume215
Issue number1
DOIs
StatePublished - Oct 20 2007

Keywords

  • Fixed points
  • Hamilton-Jacobi equations
  • Mather measures
  • Semiconcave functions

ASJC Scopus subject areas

  • Mathematics(all)

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