Uniqueness results for convex Hamilton-Jacobi equations under $p>1$ growth conditions on data

Simple item page
dc.creatorDa Lio, Francesca
dc.creatorLey, Olivier
dc.date2008-10-08
dc.date.accessioned2026-07-07T10:08:32Z
dc.date.available2026-07-07T10:08:32Z
dc.descriptionUnbounded stochastic control problems may lead to Hamilton-Jacobi-Bellman equations whose Hamiltonians are not always defined, especially when the diffusion term is unbounded with respect to the control. We obtain existence and uniqueness of viscosity solutions growing at most like $o(1+|x|^p)$ at infinity for such HJB equations and more generally for degenerate parabolic equations with a superlinear convex gradient nonlinearity. If the corresponding control problem has a bounded diffusion with respect to the control, then our results apply to a larger class of solutions, namely those growing like $O(1+|x|^p)$ at infinity. This latter case encompasses some equations related to backward stochastic differential equations.
dc.identifierhttps://arxiv.org/abs/0810.1435
dc.identifierhttp://arxiv.org/abs/0810.1435
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171026
dc.subjectAnalysis of PDEs
dc.subjectOptimization and Control
dc.subject35K65, 49L25, 35B50, 35B37, 49N10, 60H35
dc.titleUniqueness results for convex Hamilton-Jacobi equations under $p>1$ growth conditions on data
dc.typetext

Files

Collections

arXiv