Title: The Dirichlet problem for stochastic partial differential equations with nonlocal operators in $C^{1,\sigma}$ domains

Speaker: Junhee Ryu(KIAS)

Abstract: In this talk, we study a class of stochastic PDEs with nonlocal operators and spatially homogeneous colored noise in domains. The operators we consider are infinitesimal generators of (time-inhomogeneous) Lévy processes, whose Lévy measures are allowed to be very singular. We obtain the well-posedness and regularity of solutions in Sobolev spaces with the admissible spatial dimensions determined by the noise's spatial covariance.