Feller Semigroups with a First Order Ventcel’ Boundary Condition

Chapter 25 is devoted to the proof of Theorem 1.1 . Namely, we prove that the closed realization \(\mathfrak {A}_{L}\) is the infinitesimal generator of a Feller semigroup on \(C(\overline{\Omega })\) corresponding to such a diffusion phenomenon that a Markovian particle moves by continuous paths in the state space, with absorption, reflection, drift and sticking phenomena at the boundary. Moreover, we prove Remark 1.2 , that is, the domain \(D\left( \mathfrak {A}_{L}\right) \) does not depend on p, for \(N < p < \infty \) .