Eigenvalue gap theorems for a class of non symmetric elliptic operators on convex domains

TL;DR

This paper extends eigenvalue gap theorems to certain non-symmetric elliptic operators on convex domains, providing bounds based on associated Sturm-Liouville problems, thus broadening spectral analysis tools.

Contribution

It adapts the Andrews-Clutterbuck method to non-symmetric operators, establishing eigenvalue gap bounds for a new class of elliptic operators on convex domains.

Findings

Eigenvalue gap bounded below by Sturm-Liouville gap

Includes Bakry-Emery Laplacian with potential

Applicable to operators with compact support first order terms

Abstract

Adapting the method of Andrews-Clutterbuck we prove an eigenvalue gap theorem for a class of non symmetric second order linear elliptic operators on a convex domain in euclidean space. The class of operators includes the Bakry-Emery laplacian with potential and any operator with second order term the laplacian whose first order terms have coefficients with compact support in the open domain. The eigenvalue gap is bounded below by the gap of an associated Sturm-Liouville problem on a closed interval.