In this paper we prove a comparison result between viscosity subsolutions and supersolutions to Hamilton-Jacobi equations of the form u_t+H(x,Du)=0 in R^Nx(0,T) where the Hamiltonian H may be noncoercive in the gradient Du. As a consequence of the comparison result and the Perron's method we get the existence of a continuous solution of this equation.
Cutri', A., Da Lio, F. (2007). Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations. ESAIM. COCV, 13, 484-502 [10.1051/cocv:2007021].
Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations
CUTRI', ALESSANDRA;
2007-01-01
Abstract
In this paper we prove a comparison result between viscosity subsolutions and supersolutions to Hamilton-Jacobi equations of the form u_t+H(x,Du)=0 in R^Nx(0,T) where the Hamiltonian H may be noncoercive in the gradient Du. As a consequence of the comparison result and the Perron's method we get the existence of a continuous solution of this equation.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
