Aim of this paper is to show that some of the results in the weak KAM theory for 1(st) order convex Hamilton-Jacobi equations (see [11], [13]) can be extended to systems of convex Hamilton-Jacobi equations with implicit obstacles and to the obstacle problem. We obtain two results: a comparison theorem for systems lacking strict monotonicity; a representation formula for the obstacle problem involving the distance function associated to the Hamiltonian of the equation.

SYSTEMS OF CONVEX HAMILTON-JACOBI EQUATIONS WITH IMPLICIT OBSTACLES AND THE OBSTACLE PROBLEM / Camilli, Fabio; Loreti, Paola; Naoki, Yamada. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - STAMPA. - 8:4(2009), pp. 1291-1302. [10.3934/cpaa.2009.8.1291]

SYSTEMS OF CONVEX HAMILTON-JACOBI EQUATIONS WITH IMPLICIT OBSTACLES AND THE OBSTACLE PROBLEM

CAMILLI, FABIO;LORETI, Paola;
2009

Abstract

Aim of this paper is to show that some of the results in the weak KAM theory for 1(st) order convex Hamilton-Jacobi equations (see [11], [13]) can be extended to systems of convex Hamilton-Jacobi equations with implicit obstacles and to the obstacle problem. We obtain two results: a comparison theorem for systems lacking strict monotonicity; a representation formula for the obstacle problem involving the distance function associated to the Hamiltonian of the equation.
2009
large deviation hamiltonians; obstacle problem; systems of hamilton-jacobi equations; viscosity solutions
01 Pubblicazione su rivista::01a Articolo in rivista
SYSTEMS OF CONVEX HAMILTON-JACOBI EQUATIONS WITH IMPLICIT OBSTACLES AND THE OBSTACLE PROBLEM / Camilli, Fabio; Loreti, Paola; Naoki, Yamada. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - STAMPA. - 8:4(2009), pp. 1291-1302. [10.3934/cpaa.2009.8.1291]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/230539
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