1. CJM 2011 (vol 64 pp. 1289)
||Systems of Weakly Coupled Hamilton-Jacobi Equations with Implicit Obstacles|
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
Categories:35F60, 35F21, 35D40