The Neumann problem for fully nonlinear SPDE
Gassiat, Paul; Seeger, Benjamin (2021), The Neumann problem for fully nonlinear SPDE. https://basepub.dauphine.psl.eu/handle/123456789/22776
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-03481323
Series titleCahier de recherche CEREMADE, Université Paris Dauphine-PSL
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)We generalize the notion of pathwise viscosity solutions, put forward by Lions and Souganidis to study fully nonlinear stochastic partial differential equations, to equations set on a sub-domain with Neumann boundary conditions. Under a convexity assumption on the domain, we obtain a comparison theorem which yields existence and uniqueness of solutions as well as continuity with respect to the driving noise. As an application, we study the long time behaviour of a stochastically perturbed mean-curvature flow in a cylinder-like domain with right angle contact boundary condition.
Showing items related by title and author.
Ergodic problems and periodic homogenization for fully nonlinear equations in half-space type domains with Neumann boundary conditions Da Lio, Francesca; Lions, Pierre-Louis; Barles, Guy; Souganidis, Panagiotis E. (2008) Article accepté pour publication ou publié
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