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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
