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

The use of non-transversal nonlocal conditions for unbounded perturbations of two-dimensional diffusion processes, is discussed. A space as the completion of the set of infinitely differentiable functions is created for integer. Operators corresponding to nonlocal terms supported near the set are introduced. The set consists of finitely many disjoint orbits. The transformations map the curves inside the plane domain and the set of endpoints. Nonlocal conditions in the nontransversal case (a probability interpretation) is used for perturbations. Banach spaces with norms depending on the parameter are considered in the method. The Sobolev embedding theorem is used in association with Yosida theorem to define the sets used in the perturbations.