Dirichlet-to-Neumann operators on manifolds
Tim Binz · arXiv (Cornell University) · 2019
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 $\fracπ{2}$. This yields that the corresponding strictly elliptic operator with Wentzell boundary conditions generates a compact and analytic semigroups of angle $\fracπ{2}$ on the space $\mathrm{C}(\overline{M})$.