THE NEUMANN PROBLEM FOR FULLY NONLINEAR SPDE

• 成果类型: Article
• 署名作者: Gassiat, Paul; Seeger, Benjamin
• 署名单位: Universite PSL; Universite Paris-Dauphine; University of Texas System; University of Texas Austin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP2001
• 发表日期: 2024
• 页码: 1730-1788
• 关键词: partial-differential-equations; oblique derivative problems; boundary-conditions; VISCOSITY SOLUTIONS; parabolic equations; pathwise solutions; time; uniqueness; FLOW

摘要

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.