Dareiotis, K and Gerencsér, M (2017) Local L∞-estimates, weak Harnack inequality, and stochastic continuity of solutions of SPDEs. Journal of Differential Equations, 262 (1). pp. 615-632. ISSN 0022-0396
Abstract
We consider stochastic partial differential equations under minimal assumptions: the coefficients are merely bounded and measurable and satisfy the stochastic parabolicity condition. In particular, the diffusion term is allowed to be scaling-critical. We derive local supremum estimates with a stochastic adaptation of De Giorgi's iteration and establish a weak Harnack inequality for the solutions. The latter is then used to obtain pointwise almost sure continuity.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 Elsevier Inc. All rights reserved. This is an author produced version of an article published in Journal of Differential Equations. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Stochastic PDEs; Harnack's inequality; De Giorgi iteration |
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: | 06 Nov 2019 11:34 |
Last Modified: | 18 Nov 2019 14:57 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jde.2016.09.038 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:153169 |