Doubly Feller property of Brownian motions with Robin boundary condition

Abstract

In this paper, we consider first order Sobolev spaces with Robin boundary condition on unbounded Lipschitz domains. Hunt processes are associated with these spaces. We prove that the semigroup of these processes are doubly Feller. As a corollary, we provide a condition for semigroups generated by these processes being compact.

31 pages; to appear in Potential Anal