Continuous variation of eigenvalues and Gårding's inequality (Q1295489)
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scientific article; zbMATH DE number 1308148
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Continuous variation of eigenvalues and Gårding's inequality |
scientific article; zbMATH DE number 1308148 |
Statements
Continuous variation of eigenvalues and Gårding's inequality (English)
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2 September 1999
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Let \(D_t\) be a smooth 1-parameter family of elliptic selfadjoint partial differential operators on a compact manifold without boundary. We use Gårding's inequality to give a simple proof that the \(k\)th eigenvalue of \(D_t\) is continuous in \(t\).
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variation of eigenvalues
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Rayleigh-Ritz quotient
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Gärding inequality
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