Quasi-linear SPDEs in divergence form

Felix Otto, Hendrik Weber

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)1 - 22
Number of pages22
JournalStochastic Partial Differential Equations: Analysis and Computations
Early online date21 Jul 2018
DOIs
Publication statusE-pub ahead of print - 21 Jul 2018

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