The Laplacian with Wentzell-Robin boundary conditions on spaces of continuous functions

Abstract

We investigate the Laplacian Δ on a smooth bounded open set Ω ⊂ R ⁿ with Wentzell-Robin boundary condition $\beta u + \frac{{\partial u}}{{\partial v}} + \Delta u = 0$ on the boundary Γ. Under the assumption β ∈ C(Γ) with β ≥ 0, we prove that Δ generates a differentiable positive contraction semigroup on $C\left( {\bar \Omega } \right)$ and study some monotonicity properties and the asymptotic behaviour.