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Quasi-linear SPDEs in divergence-form
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Otto, Felix and Weber, Hendrik (2019) Quasi-linear SPDEs in divergence-form. Stochastics and Partial Differential Equations: Analysis and Computations, 7 (1). pp. 64-85. doi:10.1007/s40072-018-0122-0 ISSN 2194-0401.
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Official URL: https://doi.org/10.1007/s40072-018-0122-0
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.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Differential equations, Parabolic, Stochastic partial differential equations | ||||||||
| Journal or Publication Title: | Stochastics and Partial Differential Equations: Analysis and Computations | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 2194-0401 | ||||||||
| Official Date: | 5 March 2019 | ||||||||
| Dates: |
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| Volume: | 7 | ||||||||
| Number: | 1 | ||||||||
| Page Range: | pp. 64-85 | ||||||||
| DOI: | 10.1007/s40072-018-0122-0 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 28 June 2018 | ||||||||
| Date of first compliant Open Access: | 17 September 2018 | ||||||||
| RIOXX Funder/Project Grant: |
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