Optimization of the first Steklov eigenvalue in domains with holes: a shape derivate approach

DOI10.1007/s10231-006-0009-yzbMath1223.35245OpenAlexW2094315975MaRDI QIDQ997565

Julio D. Rossi, Julián Fernández Bonder, Pablo Groisman

Publication date: 7 August 2007

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-006-0009-y

zbMATH Keywords

Steklov eigenvaluesshape derivativeSobolev trace embedding

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Estimates of eigenvalues in context of PDEs (35P15) Optimization of shapes other than minimal surfaces (49Q10) Discrete approximations in optimal control (49M25)

Related Items (14)

Some optimization problems for \(p\)-Laplacian type equations ⋮ The best constant and extremals of the Sobolev embeddings in domains with holes: the \(L^{\infty }\) case ⋮ Computational Methods for Extremal Steklov Problems ⋮ Some nonlocal optimal design problems ⋮ A shape optimization problem for Steklov eigenvalues in oscillating domains ⋮ Optimal boundary holes for the Sobolev trace constant ⋮ Sharp Hardy inequalities in the half space with trace remainder term ⋮ AN OPTIMIZATION PROBLEM RELATED TO THE BEST SOBOLEV TRACE CONSTANT IN THIN DOMAINS ⋮ Estimates for the Sobolev trace constant with critical exponent and applications ⋮ Numerical studies of the Steklov eigenvalue problem via conformal mappings ⋮ OPTIMIZATION PROBLEM FOR EXTREMALS OF THE TRACE INEQUALITY IN DOMAINS WITH HOLES ⋮ An optimization problem for the first weighted eigenvalue problem plus a potential ⋮ Estimate of the spectrum deviation of the singularly perturbed Steklov problem ⋮ On the first Steklov-Dirichlet eigenvalue for eccentric annuli

Cites Work

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• On the best Sobolev trace constant and extremals in domains with holes
• Spherical symmetrization and eigenvalue estimates
• Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
• Best constants in Sobolev trace inequalities
• Minimization problems for eigenvalues of the Laplacian.
• Isolation and simplicity for the first eigenvalue of the \(p\)-Laplacian with a nonlinear boundary condition
• Symmetry properties for the extremals of the Sobolev trace embedding
• Perturbation theory for linear operators.
• Asymptotic behavior of the best Sobolev trace constant in expanding and contracting domains.
• Variation and optimization of formes. A geometric analysis
• ASYMPTOTIC BEHAVIOR OF BEST CONSTANTS AND EXTREMALS FOR TRACE EMBEDDINGS IN EXPANDING DOMAINS1*
• SYMMETRY AND SYMMETRY BREAKING FOR MINIMIZERS IN THE TRACE INEQUALITY
• Regularity of the Free Boundary in an Optimization Problem Related to the Best Sobolev Trace Constant
• ON THE EXISTENCE OF EXTREMALS FOR THE SOBOLEV TRACE EMBEDDING THEOREM WITH CRITICAL EXPONENT
• The 𝐴𝐵 program in geometric analysis: sharp Sobolev inequalities and related problems

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