Publication:
Limiting behavior of the ginzburg-landau functional

dc.contributor.coauthorJerrard, Robert L.
dc.contributor.departmentDepartment of Mathematics
dc.contributor.kuauthorSoner, Halil Mete
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-09T23:12:33Z
dc.date.issued2002
dc.description.abstractWe continue our study of the functional E-0(u) := integral(0)1/2\delu\(2) + 1/4epsilon(2) (1 - \u\(2))(2) dx, for u is an element of H-1(U;R-2), where U is a bounded, open subset of R-2. Compactness results for the scaled Jacobian of u(E) are proved under the assumption that E, (u(r)) is bounded uniformly by a function of epsilon. In addition, the Gamma limit of E(u(r))/(ln epsilon)(2) is shown to be E(upsilon) := 1/2parallel toupsilonparallel to(2)(2) + parallel todel x upsilonparallel to(.H), where upsilon is the limit of j(u(0))/\ln epsilon\, j(u(0)) = u(0) x Du(0), and parallel to(.)parallel to(.H) is the total variation of a Radon measure. These results are applied to the Ginzburg-Landau functional F-0(u,A;h(ext)) := integral(upsilon)1/2 \del(A)u\(2) + 1/4epsilon(2) (1 - \u\(2))(2) + 1/2\del x A - h(ext)\ dx, with external magnetic field h(ext) approximate to H\ln epsilon\. The Gamma limit of F-0/(ln epsilon)(2) is calculated to be F(upsilon, a; H) := 1/2[parallel toupsilon - aparallel to(2)(2) +parallel todel x upsilonparallel to(.H) + parallel todel x a - Hparallel to(2)(2)], where upsilon is as before, and a is the limit of A(p)/\ln epsilon\. (C) Elsevier Science (USA).
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue2
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuN/A
dc.description.volume192
dc.identifier.doi10.1006/jfan.2001.3906
dc.identifier.eissn1096-0783
dc.identifier.issn0022-1236
dc.identifier.quartileQ1
dc.identifier.scopus2-s2.0-0037055182
dc.identifier.urihttps://doi.org/10.1006/jfan.2001.3906
dc.identifier.urihttps://hdl.handle.net/20.500.14288/9837
dc.identifier.wos178011500011
dc.keywordsGamma limit
dc.keywordsGinzburg-landau functional
dc.keywordsBnV
dc.keywordsCompactness
dc.language.isoeng
dc.publisherElsevier
dc.relation.ispartofJournal of Functional Analysis
dc.subjectMathematics
dc.titleLimiting behavior of the ginzburg-landau functional
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorSoner, Halil Mete
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Mathematics
relation.isOrgUnitOfPublication2159b841-6c2d-4f54-b1d4-b6ba86edfdbe
relation.isOrgUnitOfPublication.latestForDiscovery2159b841-6c2d-4f54-b1d4-b6ba86edfdbe
relation.isParentOrgUnitOfPublicationaf0395b0-7219-4165-a909-7016fa30932d
relation.isParentOrgUnitOfPublication.latestForDiscoveryaf0395b0-7219-4165-a909-7016fa30932d

Files