SPD

Abstract

It is well-known that the variational approach to stochastic evolution equations leads to a L^2(\Omega;H)-theory. One of the conditions in this theory is usually referred to as the stochastic parabolicity condition. In this talk we present an L^p(\Omega;H)-wellposedness result for equations of the form d u + A u dt = B u d W, where A is a positive self-adjoint operator and B:D(A^{1/2})\to H is a certain given linear operator. Surprisingly, the condition for well-posedness depends on the integrability parameter p\in (1, \infty). In the special case that p=2 the condition reduces to the classical stochastic parabolicity condition. An example which shows the sharpness of the well-posedness condition will be discussed as well.

The talk is based on joint work with Zdzislaw Brzezniak.