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Local L-infinity-estimates, weak Harnack inequality, and stochastic continuity of solutions of SPDEs
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Univ Edinburgh, Edinburgh EH8 9YL, Midlothian, Scotland..
2017 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 262, no 1, 615-632 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2017. Vol. 262, no 1, 615-632 p.
Keyword [en]
Stochastic PDEs, Hamack's inequality, De Giorgi iteration
National Category
Mathematical Analysis
URN: urn:nbn:se:uu:diva-311476DOI: 10.1016/j.jde.2016.09.038ISI: 000388551100017OAI: oai:DiVA.org:uu-311476DiVA: diva2:1060602
Available from: 2016-12-29 Created: 2016-12-28 Last updated: 2016-12-29Bibliographically approved

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Dareiotis, Konstantinos
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