The Neumann problem for fully nonlinear SPDE

Gassiat, Paul; Seeger, Benjamin

Gassiat, Paul; Seeger, Benjamin (2021), The Neumann problem for fully nonlinear SPDE. https://basepub.dauphine.psl.eu/handle/123456789/22776

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2110.10337.pdf (511.4Kb)

Type

Document de travail / Working paper

Lien vers un document non conservé dans cette base

https://hal.archives-ouvertes.fr/hal-03481323

Date

2021

Titre de la collection

Cahier de recherche CEREMADE, Université Paris Dauphine-PSL

Ville d’édition

Paris

Métadonnées

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Auteur(s)

Gassiat, Paul
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Seeger, Benjamin

Résumé (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.