A counterexample to a conjecture by De Giorgi in large dimensions

dc.creatorPino Manresa, Manuel del
dc.creatorKowalczyk, Michal
dc.creatorWei, Juncheng
dc.date.accessioned2010-01-15T14:10:16Z
dc.date.accessioned2019-04-25T23:48:23Z
dc.date.available2010-01-15T14:10:16Z
dc.date.available2019-04-25T23:48:23Z
dc.date.created2010-01-15T14:10:16Z
dc.date.issued2008-12
dc.identifierCOMPTES RENDUS MATHEMATIQUE Volume: 346 Issue: 23-24 Pages: 1261-1266 Published: DEC 2008
dc.identifier1631-073X
dc.identifier10.1016/j.crma.2008.10.010
dc.identifierhttp://repositorio.uchile.cl/handle/2250/125143
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/2429470
dc.description.abstractWe consider the Allen-Cahn equation Delta u + u(1 - u(2)) = 0 in R-N. A celebrated conjecture by E. De Giorgi (1978) states that if u is it bounded Solution to this problem Such that partial derivative(xN) u > 0, then the level sets {u =lambda}, lambda is an element of 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.
dc.languageen
dc.publisherELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER
dc.subjectELLIPTIC-EQUATIONS
dc.titleA counterexample to a conjecture by De Giorgi in large dimensions
dc.typeArtículos de revistas


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