Uniqueness for unbounded solutions to stationary viscous Hamilton--Jacobi equations
| dc.creator | Barles, Guy | |
| dc.creator | Porretta, Alessio | |
| dc.date | 2006-01-26 | |
| dc.date.accessioned | 2026-07-07T08:26:32Z | |
| dc.date.available | 2026-07-07T08:26:32Z | |
| dc.description | We consider a class of stationary viscous Hamilton--Jacobi equations as $$ \left\{\begin{array}{l} \la u-{\rm div}(A(x) \nabla u)=H(x,\nabla u)\mbox{in }Ω, u=0{on}\partialΩ\end{array} \right. $$ where $\la\geq 0$, $A(x)$ is a bounded and uniformly elliptic matrix and $H(x,ξ)$ is convex in $ξ$ and grows at most like $|ξ|^q+f(x)$, with $1 < q < 2$ and $f \in \elle {\frac N{q'}}$. 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. $(1+|u|)^{\bar q-1} u\in \acca$, for a certain (optimal) exponent $\bar q$. This completes the recent results in \cite{GMP}, where the existence of at least one solution in this class has been proved. | |
| dc.identifier | https://arxiv.org/abs/math/0601635 | |
| dc.identifier | http://arxiv.org/abs/math/0601635 | |
| dc.identifier | Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 5, 1 (2006) 107--136 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136970 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J60, 35R05, 35Dxx | |
| dc.title | Uniqueness for unbounded solutions to stationary viscous Hamilton--Jacobi equations | |
| dc.type | text |