Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Olga Aryasova (Kyiv)
We consider an Euclidean space with semipermeable membranes on nonsmooth surfaces, for example, on the boundary of a wedge or a cone. We study the existence and uniqueness of a strong Markov process with continuous sample paths which behaves like a diffusion with given coefficients out of membranes and partially reflected on them. The question of hitting irregular points of the membranes (for instance, the vertex of a wedge) by the process plays a key role in our investigation. Besides, this problem is interesting itself.