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arXiv · 1503.04472

Local $L_\infty$-estimates, weak Harnack inequality, and stochastic continuity of solutions of SPDEs

Konstantinos Dareiotis·Máté Gerencsér
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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.

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Konstantinos Dareiotis, Máté Gerencsér. 2015-03-15. Local $L_\infty$-estimates, weak Harnack inequality, and stochastic continuity of solutions of SPDEs. https://doi.org/10.1016/j.jde.2016.09.038

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