We develop a solution theory in Hölder spaces for a quasi-linear stochastic PDE driven by an additive noise. The key ingredients are two deterministic PDE lemmas which establish a priori Hölder bounds for a parabolic equation in divergence form with irregular right-hand-side term. We apply these bounds to the case of a right-hand-side noise term which is white in time and trace class in space, to obtain stretched exponential bounds for the Hölder semi-norms of the solution.
|Pages (from-to)||1 - 22|
|Number of pages||22|
|Journal||Stochastic Partial Differential Equations: Analysis and Computations|
|Early online date||21 Jul 2018|
|Publication status||E-pub ahead of print - 21 Jul 2018|