On the Inner Radius of Nodal Domains
| dc.creator | Mangoubi, Dan | |
| dc.date | 2005-11-14 | |
| dc.date | 2006-12-20 | |
| dc.date.accessioned | 2026-07-07T09:37:52Z | |
| dc.date.available | 2026-07-07T09:37:52Z | |
| dc.description | Let M be a closed Riemannian manifold. We consider the inner radius of a nodal domain for a large eigenvalue λ. We give upper and lower bounds on the inner radius of the type C/λ^k. Our proof is based on a local behavior of eigenfunctions discovered by Donnelly and Fefferman, and a Poincaré type inequality proved by Maz'ya. Sharp lower bounds are known only in dimension two. We give an account of this case too. | |
| dc.description | Reference added, slight change in estimate in theorem 1, remark on the new proof in dim two added, to appear in Canad. Math. Bull | |
| dc.identifier | https://arxiv.org/abs/math/0511329 | |
| dc.identifier | http://arxiv.org/abs/math/0511329 | |
| dc.identifier | Canad. Math. Bull. 51 (2008), no. 2, 249--260 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160609 | |
| dc.subject | Spectral Theory | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 58J50; 35P15; 35P20 | |
| dc.title | On the Inner Radius of Nodal Domains | |
| dc.type | text |