Systems of weakly coupled Hamilton-Jacobi equations with implicit obstacles

Diogo Gomes, António Serra

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this paper we study systems of weakly coupled Hamilton-Jacobi equations with implicit obstacles that arise in optimal switching problems. Inspired by methods from the theory of viscosity solutions and weak KAM theory, we extend the notion of Aubry set for these systems. This enables us to prove a new result on existence and uniqueness of solutions for the Dirichlet problem, answering a question of F. Camilli, P. Loreti, and N. Yamada.

Original languageEnglish (US)
Pages (from-to)1289-1309
Number of pages21
JournalCanadian Journal of Mathematics
Volume64
Issue number6
DOIs
StatePublished - Dec 1 2012

Keywords

  • Hamilton-Jacobi equations
  • Switching costs
  • Viscosity solutions

ASJC Scopus subject areas

  • Mathematics(all)

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