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arXiv · 1707.01424

Quasilinear SPDEs in divergence-form

Felix Otto·Hendrik Weber
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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.

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Felix Otto, Hendrik Weber. 2017-07-05. Quasilinear SPDEs in divergence-form. https://arxiv.org/abs/1707.01424

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