Boundary value problems for elliptic pseudo-differential operators

The purpose of this paper is to study boundary value problems for elliptic pseudo-differential operators which originate from the problem of existence of Markov processes in probability theory. We prove existence and uniqueness theorems for these boundary value problems in the framework of Sobolev spaces. Our approach permits us to interpret sufficient conditions for the unique solvability of boundary value problems in terms of Markovian motion .