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Pré-Publication, Document De Travail Année : 2021

The Neumann problem for fully nonlinear SPDE

Benjamin Seeger
  • Fonction : Auteur

Résumé

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.

Dates et versions

hal-03481323 , version 1 (15-12-2021)

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Paul Gassiat, Benjamin Seeger. The Neumann problem for fully nonlinear SPDE. 2021. ⟨hal-03481323⟩
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