Special Session 53: Infinite dimensional stochastic systems and applications
Contents
In this talk we discuss a class of Sobolev spaces related to bilinear forms (e.g. Dirichlet forms) that generalize the classical spaces introduced by Mazja. They allow the immediate extension of numerous results formerly known for PDE and SPDE on Euclidean spaces or domains to abstract or highly singular spaces. Some examples in terms of SPDE will be provided. Parts of these results are based on joint work with Michael Roeckner and Alexander Teplyaev.