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, i.e. , for a certain (optimal) exponent . This completes the recent results in [15], where the existence of at least one solution in this class has been proved.
@article{ASNSP_2006_5_5_1_107_0, author = {Barles, Guy and Porretta, Alessio}, title = {Uniqueness for unbounded solutions to stationary viscous {Hamilton-Jacobi} equations}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {107--136}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 5}, number = {1}, year = {2006}, mrnumber = {2240185}, zbl = {1150.35030}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2006_5_5_1_107_0/} }
TY - JOUR AU - Barles, Guy AU - Porretta, Alessio TI - Uniqueness for unbounded solutions to stationary viscous Hamilton-Jacobi equations JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2006 SP - 107 EP - 136 VL - 5 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2006_5_5_1_107_0/ LA - en ID - ASNSP_2006_5_5_1_107_0 ER -
%0 Journal Article %A Barles, Guy %A Porretta, Alessio %T Uniqueness for unbounded solutions to stationary viscous Hamilton-Jacobi equations %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2006 %P 107-136 %V 5 %N 1 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2006_5_5_1_107_0/ %G en %F ASNSP_2006_5_5_1_107_0
Barles, Guy; Porretta, Alessio. Uniqueness for unbounded solutions to stationary viscous Hamilton-Jacobi equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 5 (2006) no. 1, pp. 107-136. http://archive.numdam.org/item/ASNSP_2006_5_5_1_107_0/
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