Minimal partitions for $p$-norms of eigenvalues
| Autor: | Beniamin Bogosel, Virginie Bonnaillie-Noël |
|---|---|
| Přispěvatelé: | Département de Mathématiques et Applications - ENS Paris (DMA), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Bogosel, Beniamin |
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
Applied Mathematics 010102 general mathematics [MATH] Mathematics [math] Equilateral triangle 01 natural sciences Square (algebra) 010101 applied mathematics Operator (computer programming) Uniform norm Optimization and Control (math.OC) FOS: Mathematics [MATH]Mathematics [math] 0101 mathematics Mathematics - Optimization and Control Eigenvalues and eigenvectors Energy (signal processing) Mathematics |
| Zdroj: | Interfaces and Free Boundaries Interfaces and Free Boundaries, European Mathematical Society, 2018, 20, pp.129-163 |
| ISSN: | 1463-9963 1463-9971 |
| Popis: | International audience; In this article we are interested in studying partitions of the square, the disk and the equilateral triangle which minimize a p-norm of eigenvalues of the Dirichlet-Laplace operator. The extremal case of the infinity norm, where we minimize the largest fundamental eigenvalue of each cell, is one of our main interests. We propose three numerical algorithms which approximate the optimal configurations and we obtain tight upper bounds for the energy, which are better than the ones given by theoretical results. A thorough comparison of the results obtained by the three methods is given. We also investigate the behavior of the minimal partitions with respect to p. This allows us to see when partitions minimizing the 1-norm and the infinity-norm are different. |
| Databáze: | OpenAIRE |
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