Speaker: Prof. Ugur Abdulla （OIST)

Abstract: 

The major problem in the Analysis of PDEs is understanding the nature of singularities of solutions to the PDEs reflecting the natural phenomena.  In this talk, I will present new Wiener-type criteria for the removability of the fundamental singularity for the parabolic PDEs. The criteria characterize the uniqueness of boundary value problems with singular data, reveal the nature of the parabolic measure of the singularity point, asymptotic laws for the conditional Markov processes, and criteria for thinness in minimal-fine topology.