On Neumann eigenfunctions in lip domains
| dc.contributor.author | Burdzy, Krzysztof | |
| dc.contributor.author | Atar, Rami | |
| dc.date.accessioned | 2005-11-30T18:25:31Z | |
| dc.date.available | 2005-11-30T18:25:31Z | |
| dc.date.issued | 2004 | |
| dc.description.abstract | A "lip domain" is a planar set lying between graphs of two Lipschitz functions with constant 1. We show that the second Neumann eigenvalue is simple in every lip domain except the square. The corresponding eigenfunction attains its maximum and minimum at the boundary points at the extreme left and right. This settles the 'hot spots' conjecture for lip domains as well as two conjectures of Jerison and Nadirashvili. Our techniques are probabilistic in nature and may have independent interest. | en |
| dc.description.sponsorship | Atar's research partially supported by the fund for the promotion of research at the Technion. Burdzy gratefull acknowledges the hospitality and financial support of Technion (Israel) and Institut Mittag-Leffler (Sweden). This research was partially supported by NSF Grant DMS-0071486 and ISF Grant 12/98. | en |
| dc.format.extent | 265834 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.citation | Atar, R. & K. Burdzy. (2004). On Neumann eigenfunctions in lip domains. Journal of the American Mathematical Society, 17(2), 243-265. | en |
| dc.identifier.uri | http://hdl.handle.net/1773/2223 | |
| dc.language.iso | en_US | |
| dc.publisher | American Mathematical Society | en |
| dc.subject | Neumann eigenfunctions | en |
| dc.subject | reflected Brownian motion | en |
| dc.subject | couplings | en |
| dc.subject | hot spots problem | en |
| dc.title | On Neumann eigenfunctions in lip domains | en |
| dc.type | Article | en |