We consider an Hamilton-Jacobi equation of the form H( x, Du) = 0 x is an element of Omega 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 ( 1) coupled with Dirichlet boundary conditions, and a stability result. The relation among Monge and Lipschitz subsolutions is also discussed.
Monge solutions for discontinuous Hamiltonians / Ariela, Briani; Davini, Andrea. - In: ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. - ISSN 1262-3377. - STAMPA. - 11:11(2005), pp. 229-251. [10.1051/cocv:2005004]
Monge solutions for discontinuous Hamiltonians
DAVINI, ANDREA
2005
Abstract
We consider an Hamilton-Jacobi equation of the form H( x, Du) = 0 x is an element of Omega 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 ( 1) coupled with Dirichlet boundary conditions, and a stability result. The relation among Monge and Lipschitz subsolutions is also discussed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
