Quasi-linear SPDEs in divergence form

Felix Otto; Hendrik Weber

doi:10.1007/s40072-018-0122-0

Quasi-linear SPDEs in divergence form

Felix Otto, Hendrik Weber

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

7 Citations (SciVal)

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 language	English
Pages (from-to)	1 - 22
Number of pages	22
Journal	Stochastic Partial Differential Equations: Analysis and Computations
Early online date	21 Jul 2018
DOIs	https://doi.org/10.1007/s40072-018-0122-0
Publication status	E-pub ahead of print - 21 Jul 2018

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10.1007/s40072-018-0122-0Licence: CC BY

https://doi.org/10.1007/s40072-018-0122-0Licence: CC BY

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title = "Quasi-linear SPDEs in divergence form",

abstract = "We develop a solution theory in H{\"o}lder spaces for a quasi-linear stochastic PDE driven by an additive noise. The key ingredients are two deterministic PDE lemmas which establish a priori H{\"o}lder 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 H{\"o}lder semi-norms of the solution.",

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AB - 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.

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DO - 10.1007/s40072-018-0122-0

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JO - Stochastic Partial Differential Equations: Analysis and Computations

JF - Stochastic Partial Differential Equations: Analysis and Computations

ER -

Quasi-linear SPDEs in divergence form

Abstract

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