Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2405.16354 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Inhaltsangabe:
- Let $Ω\subset \mathbb{R}^d$ be a bounded domain and let $λ_1, λ_2, \dots$ denote the sequence of eigenvalues of the Laplacian subject to Dirichlet boundary conditions. We consider inequalities for $λ_n$ that are independent of the domain $Ω$. A well--known such inequality follows from the Berezin--Li--Yau approach. The purpose of this paper is to point out a certain degree of flexibility in the Li--Yau approach. We use it to prove a new type of two-point inequality which are strictly stronger than what is implied by Berezin-Li-Yau itself. For example, when $d=2$, one has $ 2 λ_n + λ_{2n} \geq 10 πn/|Ω|.$