Geodesic
Systems of Weakly Coupled Hamilton-Jacobi Equations with Implicit Obstacles
Canadian journal of mathematics, Tome 64 (2012) no. 6, pp. 1289-1309

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DOI

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 $\text{KAM}$ 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.
DOI : 10.4153/CJM-2011-085-7
Mots-clés : 35F60, 35F21, 35D40, Hamilton–Jacobi equations, switching costs, viscosity solutions 
Gomes, Diogo; Serra, António. Systems of Weakly Coupled Hamilton-Jacobi Equations with Implicit Obstacles. Canadian journal of mathematics, Tome 64 (2012) no. 6, pp. 1289-1309. doi: 10.4153/CJM-2011-085-7
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     title = {Systems of {Weakly} {Coupled} {Hamilton-Jacobi} {Equations} with {Implicit} {Obstacles}},
     journal = {Canadian journal of mathematics},
     pages = {1289--1309},
     year = {2012},
     volume = {64},
     number = {6},
     doi = {10.4153/CJM-2011-085-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-085-7/}
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