L∞-estimates for Stochastic PDEs of parabolic type and applications

We will present L∞-estimates for solutions of Stochastic PDEs (SPDEs) of parabolic type obtained by techniques motivated by the works of De Giorgi and Moser in the deterministic setting. The global estimates will then be applied in order to prove solvability for a class of semilinear SPDEs, while the local estimates will be used in order to obtain a weak Harnack-type inequality for solutions of linear equations, which is in turn used to deduce information about the oscillation of the solutions. The results are from joint work with Mate Gerencser (IST, Austria).