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Monge Solutions for discontinuous Hamiltonians

Abstract : We consider an Hamilton-Jacobi equation of the form H ( x , D u ) = 0 x ∈ Ω ⊂ ℝ 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 ([see full text]) coupled with Dirichlet boundary conditions, and a stability result. The relation among Monge and Lipschitz subsolutions is also discussed.
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Contributor : Aurélien Arnoux Connect in order to contact the contributor
Submitted on : Friday, April 11, 2014 - 2:21:10 PM
Last modification on : Wednesday, May 11, 2022 - 12:06:05 PM

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Ariela Briani, Andrea Davini. Monge Solutions for discontinuous Hamiltonians. ESAIM: Control, Optimisation and Calculus of Variations, 2005, 11 (2), pp.229-251. ⟨10.1051/cocv:2005004⟩. ⟨hal-00977661⟩



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