Extremality conditions and regularity of solutions to optimal partition problems involving Laplacian eigenvalues

DOI10.1007/s00205-015-0934-2zbMath1336.49054arXiv1403.6313OpenAlexW3104159930MaRDI QIDQ261304

Hugo Tavares, Susanna Terracini, Miguel Ramos

Publication date: 23 March 2016

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.6313

zbMATH Keywords

regularityLaplacian eigenvaluesoptimal partitions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (17)

Hölder bounds and regularity of emerging free boundaries for strongly competing Schrödinger equations with nontrivial grouping ⋮ New radial solutions of strong competitive \(m\)-coupled elliptic system with general form in \(B_1(0)\) ⋮ Regularity of all minimizers of a class of spectral partition problems ⋮ On the honeycomb conjecture for a class of minimal convex partitions ⋮ Optimal partition problems for the fractional Laplacian ⋮ Segregated configurations involving the square root of the Laplacian and their free boundaries ⋮ Free boundary problems with long-range interactions: uniform Lipschitz estimates in the radius ⋮ Consistency of Dirichlet Partitions ⋮ Regularity of the optimal sets for the second Dirichlet eigenvalue ⋮ On the honeycomb conjecture for Robin Laplacian eigenvalues ⋮ Uniform bounds for strongly competing systems: the optimal Lipschitz case ⋮ Variational problems with long-range interaction ⋮ On phase separation in systems of coupled elliptic equations: asymptotic analysis and geometric aspects ⋮ Regularity of the optimal sets for some spectral functionals ⋮ Limit configurations of Schrödinger systems versus optimal partition for the principal eigenvalue of elliptic systems ⋮ Optimal partitions for Robin Laplacian eigenvalues ⋮ Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form

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