Does the stochastic parabolicity condition depend on p?
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If you have a question about this talk, please contact Mustapha Amrani.
Stochastic Partial Differential Equations (SPDEs)
It is wellknown 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 selfadjoint operator and B:D(A^{1/2}) o H is a certain given linear operator. Surprisingly, the condition for wellposedness depends on the integrability parameter pin (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 wellposedness condition will be discussed as well.
The talk is based on joint work with Zdzislaw Brzezniak.
This talk is part of the Isaac Newton Institute Seminar Series series.
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