Issoglio, E and Zahle, M (2015) Regularity of the Solutions to SPDEs in Metric Measure Spaces. Stochastic Partial Differential Equations: Analysis and Computations, 3 (2). pp. 272-289. ISSN 2194-0401
Abstract
In this paper we study the regularity of non-linear parabolic PDEs and stochastic PDEs on metric measure spaces admitting heat kernel estimates. In particular we consider mild function solutions to abstract Cauchy problems and show that the unique solution is Hölder continuous in time with values in a suitable fractional Sobolev space. As this analysis is done via a-priori estimates, we can apply this result to stochastic PDEs on metric measure spaces and solve the equation in a pathwise sense for almost all paths. The main example of noise term is of fractional Brownian type and the metric measure spaces can be classical as well as given by various fractal structures. The whole approach is low dimensional and works for spectral dimensions less than 4.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 Springer Science+Business Media. This is an author produced version of a paper published in Stochastic Partial Differential Equations: Analysis and Computations. Uploaded in accordance with the publisher's self-archiving policy. The final publication is available at Springer via https://dx.doi.org/10.1007/s40072-015-0048-8. |
Keywords: | Stochastic nonlinear PDEs; Regularity of solutions; Pathwise solutions; Semigroups; Metric measure spaces; Fractals |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 05 May 2015 14:01 |
Last Modified: | 17 Jan 2018 18:45 |
Published Version: | https://dx.doi.org/10.1007/s40072-015-0048-8 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s40072-015-0048-8 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:85541 |