Uniform stability of the Dirichlet spectrum for rough outer perturbations
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Bibliographic record
Abstract
The goal of this paper is to study the Dirichlet eigenvalues of bounded domains \Omega\subset\Omega' . With a local spectral stability requirement on \Omega , we show that the difference of the Dirichlet eigenvalues of \Omega' and \Omega is explicitly controlled from above in terms of the first eigenvalue of \Omega'\setminus\bar{\Omega} and of geometric constants depending on the inner domain \Omega . In particular, \Omega' can be an arbitrary bounded domain.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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