Uniqueness for unbounded solutions to stationary viscous Hamilton-Jacobi equations
Guy Barles, Alessio Porretta (2006)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We consider a class of stationary viscous Hamilton-Jacobi equations aswhere , is a bounded and uniformly elliptic matrix and is convex in and grows at most like , with and . Under such growth conditions solutions are in general unbounded, and there is not uniqueness of usual weak solutions. We prove that uniqueness holds in the restricted class of solutions satisfying a suitable energy-type estimate, , for a certain (optimal) exponent . This completes the...