Optimization of Neumann Eigenvalues under convexity and geometric constraints
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916117122908160 |
|---|---|
| author | Bogosel, Beniamin Henrot, Antoine Michetti, Marco |
| author_facet | Bogosel, Beniamin Henrot, Antoine Michetti, Marco |
| contents | In this paper we study optimization problems for Neumann eigenvalues $μ_k$ among convex domains with a constraint on the diameter or the perimeter. We work mainly in the plane, though some results are stated in higher dimension. We study the existence of an optimal domain in all considered cases. We also consider the case of the unit disk, giving values of the index $k$ for which it can be or cannot be extremal. We give some numerical examples for small values of $k$ that lead us to state some conjectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04117 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimization of Neumann Eigenvalues under convexity and geometric constraints Bogosel, Beniamin Henrot, Antoine Michetti, Marco Analysis of PDEs Optimization and Control 35P15 In this paper we study optimization problems for Neumann eigenvalues $μ_k$ among convex domains with a constraint on the diameter or the perimeter. We work mainly in the plane, though some results are stated in higher dimension. We study the existence of an optimal domain in all considered cases. We also consider the case of the unit disk, giving values of the index $k$ for which it can be or cannot be extremal. We give some numerical examples for small values of $k$ that lead us to state some conjectures. |
| title | Optimization of Neumann Eigenvalues under convexity and geometric constraints |
| topic | Analysis of PDEs Optimization and Control 35P15 |
| url | https://arxiv.org/abs/2402.04117 |