Dirichlet-to-Neumann operators on manifolds

Abstract

We consider the Dirichlet-to-Neumann operator associated to a strictly elliptic operator on the space $\mathrm{C}(\partial M)$ of continuous functions on the boundary $\partial M$ of a compact manifold $\overline{M}$ with boundary. We prove that it generates an analytic semigroup of angle $\frac{\pi}{2}$. This yields that the corresponding strictly elliptic operator with Wentzell boundary conditions generates a compact and analytic semigroups of angle $\frac{\pi}{2}$ on the space $\mathrm{C}(\overline{M})$.