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dc.contributor.authorKatzourakis, N.I.
dc.date.accessioned2017-02-21T08:18:18Z
dc.date.available2017-02-21T08:18:18Z
dc.date.issued2013-12-31
dc.identifier.issn1631-073X
dc.identifier.urihttp://hdl.handle.net/20.500.11824/536
dc.description.abstractGiven a map u:Ω⊆Rn→RN, the ∞-Laplacian is the system:(1)δ∞u:=(Du⊗Du+|Du|2[Du]⊥⊗I):D2u=0 and arises as the "Euler-Lagrange PDE" of the supremal functional E∞(u,Ω)={norm of matrix}Du{norm of matrix}L∞(Ω). (1) is the model PDE of the vector-valued Calculus of Variations in L∞ and first appeared in the author's recent work [10-14]. Solutions to (1) present a natural phase separation with qualitatively different behaviour on each phase. Moreover, on the interfaces the coefficients of (1) are discontinuous. Herein we construct new explicit smooth solutions for n=N=2, for which the interfaces have triple junctions and non-smooth corners. The high complexity of these solutions provides further understanding of the PDE (1) and limits what might be true in future regularity considerations of the interfaces.
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dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.titleExplicit 2D ∞-harmonic maps whose interfaces have junctions and corners
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1016/j.crma.2013.07.028
dc.relation.publisherversionhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84887220553&doi=10.1016%2fj.crma.2013.07.028&partnerID=40&md5=ffd7d7e0c21838eea207462e2f76d0bc
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/publishedVersionen_US
dc.journal.titleComptes Rendus Mathematiqueen_US


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