Quasilinear SPDEs in divergence-form
Analysis of PDEs
2017-07-06 v1 Probability
Abstract
We develop a solution theory in H\"older spaces for a quasilinear stochastic PDE driven by an additive noise. The key ingredients are two deterministic PDE Lemmas which establish a priori H\"older bounds for an equation with irregular right hand side written in divergence form. We apply these deterministic bounds to the case of a noise term which is white in time and trace class in space to obtain stretched exponential bounds for the H\"older semi-norms of the solution for the stochastic equation.
Keywords
Cite
@article{arxiv.1707.01424,
title = {Quasilinear SPDEs in divergence-form},
author = {Felix Otto and Hendrik Weber},
journal= {arXiv preprint arXiv:1707.01424},
year = {2017}
}
Comments
17 pages