Title    name Stochastic Partial Differential Equations and the Related Fields.     Title On the Sobolev regularity of the stochastic heat equation on a polygonal domain   Speaker Felix Lindner   Date 2012-06-27   Host   Place NIMS   File     Abstract : Based on a classical result by P. Grisvard we show that the solution of the stochastic heat equation with zero Dirichlet boundary condition on a polygonal domain can be decomposed into a regular part with maximal spatial Sobolev regularity and a singular part whose spatial Sobolev regularity is limited due to the shape of the domain. In the context of adaptive approximation of SPDEs this complements a recent result about the spatial Besov regularity of parabolic SPDEs on Lipschitz domains [Studia Math. 207 (2011), 197-234].

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