Uniform bounds for eigenfunctions of the Laplacian on manifolds with boundary
| dc.creator | Grieser, D. | |
| dc.date | 2001-03-13 | |
| dc.date | 2002-05-22 | |
| dc.date.accessioned | 2026-07-07T04:40:37Z | |
| dc.date.available | 2026-07-07T04:40:37Z | |
| dc.description | Let $u$ be an eigenfunction of the Laplacian on a compact manifold with boundary, with Dirichlet or Neumann boundary conditions, and let $-λ^2$ be the corresponding eigenvalue. We consider the problem of estimating the maximum of $u$ in terms of $λ$, for large $λ$, assuming $u$ is $L^2$-normalized. We prove that $\max_M u\leq C_M λ^{(n-1)/2}$, which is optimal for some $M$. Our proof simplifies some of the arguments used before for such problems. In order to make the article accessible to non-specialists, we review the 'wave equation method' (which has become standard in asymptotic eigenvalue problems) and discuss some special cases which may be handled by more direct methods. | |
| dc.description | 12 pages, correction of minor errors in Sections 4, 5; to appear in Comm. PDE | |
| dc.identifier | https://arxiv.org/abs/math/0103080 | |
| dc.identifier | http://arxiv.org/abs/math/0103080 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61083 | |
| dc.subject | Spectral Theory | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35P20 | |
| dc.title | Uniform bounds for eigenfunctions of the Laplacian on manifolds with boundary | |
| dc.type | text |