On the Existence of Feller Semigroups with Boundary Conditions, II

This paper is devoted to the functional analytic approach to the problem of construction of Feller semigroups with Ventcel′ (Wentzell) boundary conditions. The problem of construction of Feller semigroups has never before been studied in the characteristic case. In this paper we consider the characteristic case. Intuitively, our result may be stated as follows: We can construct a Feller semigroup corresponding to such a diffusion phenomenon that one of the reflection and viscosity phenomena occurs at each point of the boundary.