Strictly elliptic operators with Dirichlet boundary conditions on spaces of continuous functions on manifolds

TL;DR

This paper investigates strictly elliptic differential operators with Dirichlet boundary conditions on continuous functions over compact manifolds, establishing their sectoriality with the optimal angle of π/2.

Contribution

It proves the sectoriality of such operators on continuous function spaces over manifolds, providing optimal angle results.

Findings

Proves sectoriality with angle π/2 for elliptic operators on manifolds.

Establishes foundational spectral properties of these operators.

Extends analysis to operators on continuous functions over manifolds.

Abstract

We study strictly elliptic differential operators with Dirichlet boundary conditions on the space $\mathrm{C}(\overline{M})$ of continuous functions on a compact, Riemannian manifold $\overline{M}$ with boundary and prove sectoriality with optimal angle $\frac{\pi}{2}$.