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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

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-03481323
Date
2021
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
43
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Author(s)
Gassiat, Paul
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Seeger, Benjamin
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.