Systems of Weakly Coupled Hamilton-Jacobi Equations with Implicit Obstacles
Printed: Dec 2012
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.
Hamilton-Jacobi equations, switching costs, viscosity solutions
35F60 - Boundary value problems for nonlinear first-order systems
35F21 - Hamilton-Jacobi equations
35D40 - Viscosity solutions