| Author | dc.contributor.author | Pino Manresa, Manuel del | |
| Author | dc.contributor.author | Kowalczyk, Michal | es_CL |
| Author | dc.contributor.author | Wei, Juncheng | es_CL |
| Admission date | dc.date.accessioned | 2010-01-13T13:23:50Z | |
| Available date | dc.date.available | 2010-01-13T13:23:50Z | |
| Publication date | dc.date.issued | 2008-12 | |
| Cita de ítem | dc.identifier.citation | COMPTES RENDUS MATHEMATIQUE Volume: 346 Issue: 23-24 Pages: 1261-1266 Published: DEC 2008 | en_US |
| Identifier | dc.identifier.issn | 1631-073X | |
| Identifier | dc.identifier.uri | https://repositorio.uchile.cl/handle/2250/125101 | |
| Abstract | dc.description.abstract | We consider the Allen–Cahn equation
u +u
1− u2
=0 inRN.
A celebrated conjecture by E. De Giorgi (1978) states that if u is a bounded solution to this problem such that ∂xNu>0, then the
level sets {u=λ}, λ ∈R, must be hyperplanes at least if N 8. We construct a family of solutions which shows that this statement
does not hold true for N 9. | en_US |
| Patrocinador | dc.description.sponsorship | The first author has been partly supported by research grants Fondecyt 1070389 and FONDAP, Chile. The second
author has been supported by Fondecyt grant 1050311, Nucleus Millennium grant P04-069-F, and FONDAP, Chile.
The research of the third author is partially supported by an Earmarked Grant from RGC of Hong Kong and a Direct
Grant from CUHK. | en_US |
| Lenguage | dc.language.iso | en | en_US |
| Publisher | dc.publisher | ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER | en_US |
| Keywords | dc.subject | ELLIPTIC-EQUATIONS | en_US |
| Título | dc.title | A counterexample to a conjecture by De Giorgi in large dimensions | en_US |
| Document type | dc.type | Artículo de revista | |
