Existence and non-existence results for minimizers of the Ginzburg-Landau energy with prescribed degrees

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dc.contributor.authorDos Santos, Mickael
dc.contributor.authorRodiac, Remy
dc.date.accessioned2024-01-10T12:05:22Z
dc.date.available2024-01-10T12:05:22Z
dc.date.issued2016
dc.description.abstractLet D = Omega\(omega) over bar subset of R-2 be a smooth annular type domain. We consider the simplified Ginzburg-Landau energy E-epsilon (u) = 1/2 integral (D) vertical bar del u vertical bar(2) + 1/4s(2) integral (D) (1 - vertical bar u vertical bar(2))(2) where u : D -> C, and look for minimizers of E-epsilon with prescribed degrees deg (u, partial derivative Omega) = p, deg (u, partial derivative omega) = q on the boundaries of the domain. For large epsilon and for balanced degrees (i.e. p = q), we obtain existence of minimizers for domains with large capacity ( corresponding to thin annulus). We also prove non-existence of minimizers of E-epsilon, for large epsilon, if p not equal q, pq > 0 and if D is a circular annulus with large capacity. Our approach relies on similar results obtained for the Dirichlet energy E-infinity (u) = 1/2 integral (D) vertical bar del u vertical bar(2), on a previous existence result obtained by Berlyand and Golovaty and on a technique developed by Misiats.
dc.fechaingreso.objetodigital2024-05-14
dc.format.extent31 páginas
dc.fuente.origenWOS
dc.identifier.doi10.1142/S0219199716500176
dc.identifier.eissn1793-6683
dc.identifier.issn0219-1997
dc.identifier.urihttps://doi.org/10.1142/S0219199716500176
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/75995
dc.identifier.wosidWOS:000381203800015
dc.information.autorucMatemática;Rodiac R;S/I;1040236
dc.issue.numero5
dc.language.isoen
dc.nota.accesocontenido parcial
dc.publisherWORLD SCIENTIFIC PUBL CO PTE LTD
dc.revistaCOMMUNICATIONS IN CONTEMPORARY MATHEMATICS
dc.rightsacceso restringido
dc.subjectGinzburg-Landau energy
dc.subjectprescribed degrees
dc.subjectlack of compactness
dc.subjectBOUNDARY
dc.subjectUNIQUENESS
dc.titleExistence and non-existence results for minimizers of the Ginzburg-Landau energy with prescribed degrees
dc.typeartículo
dc.volumen18
sipa.codpersvinculados1040236
sipa.indexWOS
sipa.indexScopus
sipa.trazabilidadCarga SIPA;09-01-2024
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