Unbounded perturbations of two-dimensional diffusion processes with nonlocal boundary conditions (Q957819)

Let \(G\subset \mathbb R^2\) be a bounded domain and \(K\) a finite subset of the boundary \(\partial G\). Let \(\Gamma_i\) be open connected such that \(\partial G\setminus K= \bigcup_{i=1}^N \Gamma_i\). This paper investigates perturbations of a uniform elliptic \(P_0\) differential operator with nonlocal boundary conditions like \(u- B_i u +\psi_i\) on \(\Gamma_i\), \(1\leq i\leq N.\) Under certain regularity conditions on \(P_0\) and a perturbation operator \(P_1\), it is proved that \(P_0+P_1\) has a proper closure which generates a Feller semigroup. Since \(P_0\) is uniform elliptic, it should be reasonable to ask further for the strong Feller property.