Qualitative and Numerical Analysis of a Spectral Problem with Perimeter Constraint

DOI10.1137/140999530zbMath1335.49070OpenAlexW2283883966MaRDI QIDQ2796007

Edouard Oudet, Beniamin Bogosel

Publication date: 23 March 2016

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: http://hal.univ-grenoble-alpes.fr/hal-02009510/file/gamma-conv-perim%20%281%29.pdf

zbMATH Keywords

eigenvaluesoptimality conditionsshape optimization\(\Gamma\)-convergenceperimeter constraintDirichlet Laplace operator

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Methods involving semicontinuity and convergence; relaxation (49J45) Optimization of shapes other than minimal surfaces (49Q10) Numerical methods of relaxation type (49M20) Variational methods for eigenvalues of operators (49R05)

Related Items (11)

A two-stage method for piecewise-constant solution for Fredholm integral equations of the first kind ⋮ Optimisation of eigenvalues of the Dirichlet Laplacian with a surface area restriction ⋮ A level set method for Laplacian eigenvalue optimization subject to geometric constraints ⋮ Computational Methods for Extremal Steklov Problems ⋮ Regularity of minimizers of shape optimization problems involving perimeter ⋮ Regularity in shape optimization under convexity constraint ⋮ Phase field approach to optimal packing problems and related Cheeger clusters ⋮ Maximising Neumann eigenvalues on rectangles ⋮ Extremal p -Laplacian eigenvalues ⋮ Computation of free boundary minimal surfaces via extremal Steklov eigenvalue problems ⋮ Phase-field methods for spectral shape and topology optimization

Uses Software

• minFunc

Cites Work

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• Optimal Partitions for Eigenvalues
• Approximation of Partitions of Least Perimeter by Γ-Convergence: Around Kelvin’s Conjecture
• Minimization of $\lambda_{2}(\Omega)$ with a perimeter constraint
• Numerical minimization of eigenmodes of a membrane with respect to the domain

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