On the P\'olya conjecture for the Neumann problem in planar convex domains
| Autor: | Filonov, N. |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Denote by $N_{\cal N} (\Omega,\lambda)$ the counting function of the spectrum of the Neumann problem in the domain $\Omega$ on the plane. G. P\'olya conjectured that $N_{\cal N} (\Omega,\lambda) \ge (4\pi)^{-1} |\Omega| \lambda$. We prove that for convex domains $N_{\cal N} (\Omega,\lambda) \ge (2 \sqrt 3 \,j_0^2)^{-1} |\Omega| \lambda$. Here $j_0$ is the first zero of the Bessel function $J_0$. |
| Databáze: | arXiv |
| Externí odkaz: |
|