Geodesic
Representation of viscosity solutions of Hamilton-Jacobi equations
Minimax theory and its applications, Tome 1 (2016) no. 1
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Hamilton Jacobi equations of the form H(x,u,Du) = 0 are considered with H(x,r,p) non decreasing in r and quasiconvex in p. A viscosity solution may be represented as the value function of a calculus of variations or control problem in L∞, i.e., as a minimax problem. For time dependent problems of the form ut + H(t,x,u,Du) = 0 we require that H(t,x,r,p) is convex in p and nondecreasing in r. The viscosity solution is then given as the value of an L∞ problem.
Mots-clés : Quasiconvex, Hamilton-Jacobi, representation 
@article{MTA_2016_1_1_a3,
     author = {E. N. Barron},
     title = {Representation of viscosity solutions of {Hamilton-Jacobi} equations},
     journal = {Minimax theory and its applications},
     year = {2016},
     volume = {1},
     number = {1},
     zbl = {1336.35112},
     url = {http://geodesic.mathdoc.fr/item/MTA_2016_1_1_a3/}
}
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E. N. Barron. Representation of viscosity solutions of Hamilton-Jacobi equations. Minimax theory and its applications, Tome 1 (2016) no. 1. http://geodesic.mathdoc.fr/item/MTA_2016_1_1_a3/