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Systems of Weakly Coupled Hamilton-Jacobi Equations with Implicit Obstacles

  Published:2011-11-03
 Printed: Dec 2012
  • Diogo Gomes,
    Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
  • António Serra,
    Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
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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.
Keywords: Hamilton-Jacobi equations, switching costs, viscosity solutions Hamilton-Jacobi equations, switching costs, viscosity solutions
MSC Classifications: 35F60, 35F21, 35D40 show english descriptions Boundary value problems for nonlinear first-order systems
Hamilton-Jacobi equations
Viscosity solutions
35F60 - Boundary value problems for nonlinear first-order systems
35F21 - Hamilton-Jacobi equations
35D40 - Viscosity solutions
 

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