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;
2009-01-01
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.File in questo prodotto:
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