A Surgery Result for the Spectrum of the Dirichlet Laplacian
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Publication:3455233
DOI10.1137/140992448zbMath1331.49062arXiv1410.5179OpenAlexW1816855998MaRDI QIDQ3455233
Publication date: 4 December 2015
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1410.5179
Estimates of eigenvalues in context of PDEs (35P15) Existence of solutions for minimax problems (49J35) Optimization of shapes other than minimal surfaces (49Q10) Variational methods for eigenvalues of operators (49R05)
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Cites Work
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- Existence of minimizers for spectral problems
- Estimates for the torsion function and Sobolev constants
- Existence and regularity of minimizers for some spectral functionals with perimeter constraint
- On the Schrödinger equation and the eigenvalue problem
- Une méthode de comparaison isoperimetrique de fonctionnelles de domaines de la physique mathématique. I. Premiere partie: une demonstration de la conjecture isoperimetrique \(P\lambda^2\geq\pi j^4_0/2\) de Polya et Szegö
- An existence result for a class of shape optimization problems
- The universal eigenvalue bounds of Payne-Pólya-Weinberger, Hile-Protter, and H. C. Yang
- Minimization of the \(k\)-th eigenvalue of the Dirichlet Laplacian
- Lipschitz regularity of the eigenfunctions on optimal domains
- Variational methods in shape optimization problems
- On the torsion function with Robin or Dirichlet boundary conditions
- Spectral Optimization Problems for Potentials and Measures
- On the minimization of Dirichlet eigenvalues
- Minimization of $\lambda_{2}(\Omega)$ with a perimeter constraint
