Lower bounds for the spectrum of the Laplace and Stokes operators
Alexei A. Ilyin
TL;DR
This paper establishes improved lower bounds for the eigenvalues of the Laplace and Stokes operators, extending existing estimates and generalizing to higher-order operators.
Contribution
It introduces Berezin--Li--Yau-type lower bounds with additional terms for the Stokes operator eigenvalues and enhances previous bounds for the Laplace operator, including generalizations.
Findings
Improved lower bounds for Laplace eigenvalues.
New bounds for Stokes operator eigenvalues.
Extensions to higher-order differential operators.
Abstract
We prove Berezin--Li--Yau-type lower bounds with additional term for the eigenvalues of the Stokes operator and improve the previously known estimates for the Laplace operator. Generalizations to higher-order operators are given.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Harmonic Analysis Research · Advanced Mathematical Modeling in Engineering