Strictly elliptic operators with generalized Wentzell boundary conditions on continuous functions on manifolds with boundary

TL;DR

This paper proves that certain elliptic operators with generalized boundary conditions generate analytic semigroups on continuous functions over compact manifolds with boundary, advancing the understanding of boundary value problems.

Contribution

It establishes the generation of analytic semigroups by strictly elliptic operators with generalized Wentzell boundary conditions on continuous functions on manifolds with boundary.

Findings

Elliptic operators with generalized Wentzell boundary conditions generate analytic semigroups.

The results apply to continuous functions on compact manifolds with boundary.

The semigroups have an angle of C0/2, indicating strong regularity properties.

Abstract

We prove that strictly elliptic operators with generalized Wentzell boundary conditions generate analytic semigroups of angle $\frac{\pi}{2}$ on the space of continuous function on a compact manifold with boundary.