Monge Solutions for Discontinuous Hamiltonians
نویسندگان
چکیده
We consider an Hamilton-Jacobi equation of the form H(x,Du) = 0 x ∈ Ω ⊂ R , (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. Mathematics Subject Classification. 49J25, 35C15, 35R05. Received January 15, 2004.
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تاریخ انتشار 2005