Monge solutions for discontinuous Hamiltonians
Dipartimento di Matematica, Università di Pisa Lago B. Pontecorvo 5, 56127 Pisa, Italy; firstname.lastname@example.org; email@example.com
We consider an Hamilton-Jacobi equation of the form 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.
Mathematics Subject Classification: 49J25 / 35C15 / 35R05
Key words: Viscosity solution / lax formula / Finsler metric.
© EDP Sciences, SMAI, 2005