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arXiv · 2110.10337

The Neumann problem for fully nonlinear SPDE

Paul Gassiat·Benjamin Seeger
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Abstract

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.

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Paul Gassiat, Benjamin Seeger. 2021-10-20. The Neumann problem for fully nonlinear SPDE. https://arxiv.org/abs/2110.10337

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