The Allegretto-Piepenbrink Theorem for strongly local forms
Daniel Lenz, Peter Stollmann, Ivan Veseli\'c
TL;DR
This paper explores the relationship between positive weak solutions of PDEs and spectral properties of associated operators, extending classical results to strongly local forms.
Contribution
It introduces a new version of the Allegretto-Piepenbrink theorem applicable to strongly local forms, broadening the theoretical framework.
Findings
Established a spectral criterion for positive weak solutions
Extended classical theorems to strongly local forms
Provided new insights into PDE spectral theory
Abstract
The existence of positive weak solutions is related to spectral information on the corresponding partial differential operator.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Algebra and Geometry · Geometry and complex manifolds