Reverse isoperimetric inequality for the lowest Robin eigenvalue of a triangle
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916595886981120 |
|---|---|
| author | Krejcirik, David Lotoreichik, Vladimir Vu, Tuyen |
| author_facet | Krejcirik, David Lotoreichik, Vladimir Vu, Tuyen |
| contents | We consider the Laplace operator on a triangle, subject to attractive Robin boundary conditions. We prove that the equilateral triangle is a local maximiser of the lowest eigenvalue among all triangles of a given area provided that the negative boundary parameter is sufficiently small in absolute value, with the smallness depending on the area only. Moreover, using various trial functions, we obtain sufficient conditions for the global optimality of the equilateral triangle under fixed area constraint in the regimes of small and large couplings. We also discuss the constraint of fixed perimeter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_03235 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Reverse isoperimetric inequality for the lowest Robin eigenvalue of a triangle Krejcirik, David Lotoreichik, Vladimir Vu, Tuyen Optimization and Control Mathematical Physics Analysis of PDEs Spectral Theory We consider the Laplace operator on a triangle, subject to attractive Robin boundary conditions. We prove that the equilateral triangle is a local maximiser of the lowest eigenvalue among all triangles of a given area provided that the negative boundary parameter is sufficiently small in absolute value, with the smallness depending on the area only. Moreover, using various trial functions, we obtain sufficient conditions for the global optimality of the equilateral triangle under fixed area constraint in the regimes of small and large couplings. We also discuss the constraint of fixed perimeter. |
| title | Reverse isoperimetric inequality for the lowest Robin eigenvalue of a triangle |
| topic | Optimization and Control Mathematical Physics Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2204.03235 |