Local L-infinity-estimates, weak Harnack inequality, and stochastic continuity of solutions of SPDEs
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
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.
Stochastic PDEs, Hamack's inequality, De Giorgi iteration
IdentifiersURN: urn:nbn:se:uu:diva-311476DOI: 10.1016/j.jde.2016.09.038ISI: 000388551100017OAI: oai:DiVA.org:uu-311476DiVA: diva2:1060602