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Sharp energy estimates for nonlinear fractional diffusion equations
dc.contributor.author | Cabré Vilagut, Xavier |
dc.contributor.author | Cinti, Eleonora |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2014-02-27T11:34:39Z |
dc.date.created | 2014-01 |
dc.date.issued | 2014-01 |
dc.identifier.citation | Cabre, X.; Cinti, E. Sharp energy estimates for nonlinear fractional diffusion equations. "Calculus of variations and partial differential equations", Gener 2014, vol. 49, núm. 1-2, p. 233-269. |
dc.identifier.issn | 0944-2669 |
dc.identifier.uri | http://hdl.handle.net/2117/21782 |
dc.description.abstract | We study the nonlinear fractional equation (−Δ)su=f(u) in Rn, for all fractions 0<s<1 and all nonlinearities f . For every fractional power s∈(0,1) , we obtain sharp energy estimates for bounded global minimizers and for bounded monotone solutions. They are sharp since they are optimal for solutions depending only on one Euclidian variable. As a consequence, we deduce the one-dimensional symmetry of bounded global minimizers and of bounded monotone solutions in dimension n=3 whenever 1/2≤s<1 . This result is the analogue of a conjecture of De Giorgi on one-dimensional symmetry for the classical equation −Δu=f(u) in Rn . It remains open for n=3 and s<1/2 , and also for n≥4 and all s . |
dc.format.extent | 37 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.lcsh | Differential equations, Partial |
dc.subject.other | Fractional laplacian |
dc.subject.other | Energy estimates |
dc.subject.other | Symmetry properties |
dc.title | Sharp energy estimates for nonlinear fractional diffusion equations |
dc.type | Article |
dc.subject.lemac | Equacions diferencials parcials |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.identifier.doi | 10.1007/s00526-012-0580-6 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::35 Partial differential equations::35R Miscellaneous topics involving partial differential equations |
dc.subject.ams | Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions |
dc.relation.publisherversion | http://link.springer.com/article/10.1007%2Fs00526-012-0580-6 |
dc.rights.access | Restricted access - publisher's policy |
local.identifier.drac | 13065278 |
dc.description.version | Postprint (published version) |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/FP7/258685/EU/Analysis of optimal sets and optimal constants: old questions and new results/ANOPTSETCON |
dc.date.lift | 10000-01-01 |
local.citation.author | Cabre, X.; Cinti, E. |
local.citation.publicationName | Calculus of variations and partial differential equations |
local.citation.volume | 49 |
local.citation.number | 1-2 |
local.citation.startingPage | 233 |
local.citation.endingPage | 269 |
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