Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations

Cutrì, Alessandra; Lio, Francesca Da

ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 3, pp. 484-502.

In this paper we prove a comparison result between semicontinuous viscosity subsolutions and supersolutions to Hamilton-Jacobi equations of the form $u_t+H(x,Du)=0$ in ${ℝ}^n\times (0,T)$ 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.

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