Multiphase Shape Optimization Problems

DOI10.1137/130917272zbMath1312.49050arXiv1310.2448OpenAlexW2126397909MaRDI QIDQ5244631

Dorin Bucur, Bozhidar Velichkov

Publication date: 27 March 2015

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

Full work available at URL: https://arxiv.org/abs/1310.2448

zbMATH Keywords

eigenvaluesoptimal partitionsmultiphase shape optimization

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Methods involving semicontinuity and convergence; relaxation (49J45) Eigenvalue problems for linear operators (47A75) Optimization of shapes other than minimal surfaces (49Q10) Variational methods for eigenvalues of operators (49R05)

Related Items (18)

A minimal surface criterion for graph partitioning ⋮ Two- and multi-phase quadrature surfaces ⋮ Optimal partition problems for the fractional Laplacian ⋮ Regularity of minimizers of shape optimization problems involving perimeter ⋮ Consistency of Dirichlet Partitions ⋮ A free boundary approach to shape optimization problems ⋮ Uniqueness of a solution to a general class of discrete system defined on connected graphs ⋮ Cheeger \(N\)-clusters ⋮ Convergence of the finite difference scheme for a general class of the spatial segregation of reaction-diffusion systems ⋮ Lipschitz regularity of the eigenfunctions on optimal domains ⋮ Free boundary regularity for a multiphase shape optimization problem ⋮ Optimal partitions for Robin Laplacian eigenvalues ⋮ Multiphase free discontinuity problems: monotonicity formula and regularity results ⋮ Existence and regularity of minimizers for some spectral functionals with perimeter constraint ⋮ Regularity of the free boundary for the two-phase Bernoulli problem ⋮ Shape optimization problems in control form ⋮ Existence and regularity of optimal shapes for elliptic operators with drift ⋮ Efficient algorithm for optimizing spectral partitions

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