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1. CJM 2011 (vol 64 pp. 1289)

Gomes, Diogo; Serra, António
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

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