Monge solutions for discontinuous hamiltonians
ESAIM: Control, Optimisation and Calculus of Variations, Volume 11 (2005) no. 2, pp. 229-251.

We consider an Hamilton-Jacobi equation of the form

H(x,Du)=0xΩ N ,(1)
where H(x,p) is assumed Borel measurable and quasi-convex in p. The notion of Monge solution, introduced by Newcomb and Su, is adapted to this setting making use of suitable metric devices. We establish the comparison principle for Monge sub and supersolution, existence and uniqueness for equation (1) coupled with Dirichlet boundary conditions, and a stability result. The relation among Monge and Lipschitz subsolutions is also discussed.

DOI: 10.1051/cocv:2005004
Classification: 49J25,  35C15,  35R05
Keywords: viscosity solution, lax formula, Finsler metric
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     title = {Monge solutions for discontinuous hamiltonians},
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Briani, Ariela; Davini, Andrea. Monge solutions for discontinuous hamiltonians. ESAIM: Control, Optimisation and Calculus of Variations, Volume 11 (2005) no. 2, pp. 229-251. doi : 10.1051/cocv:2005004. http://archive.numdam.org/articles/10.1051/cocv:2005004/

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