Recent Existence Results for Spectral Problems

DOI10.1007/978-3-319-17563-8_8zbMath1329.49089OpenAlexW2460457069MaRDI QIDQ3466793

Dario Mazzoleni

Publication date: 25 January 2016

Published in: New Trends in Shape Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-17563-8_8

zbMATH Keywords

eigenvaluesshape optimizationDirichlet Laplacian

Mathematics Subject Classification ID

Optimization of shapes other than minimal surfaces (49Q10) Variational methods for eigenvalues of operators (49R05)

Related Items (1)

Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domains

Cites Work

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• Existence of minimizers for spectral problems
• On the characterization of the compact embedding of Sobolev spaces
• Spectral optimization problems
• Existence and regularity of minimizers for some spectral functionals with perimeter constraint
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Wiener criteria and energy decay for relaxed Dirichlet problems
• Wiener's criterion and \(\Gamma\)-convergence
• An existence result for a class of shape optimization problems
• Minimization problems for eigenvalues of the Laplacian.
• Uniform concentration-compactness for Sobolev spaces on variable domains
• Minimization of the \(k\)-th eigenvalue of the Dirichlet Laplacian
• Lipschitz continuity of state functions in some optimal shaping
• Regularity of the optimal shape for the first eigenvalue of the Laplacian with volume and inclusion constraints
• Spectral optimization problems with internal constraint
• Proof of the Payne-Pólya-Weinberger conjecture
• Minimization of the third eigenvalue of the Dirichlet Laplacian

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