dc.contributor.author Katzourakis, N.I. dc.date.accessioned 2016-06-13T13:33:49Z dc.date.available 2016-06-13T13:33:49Z dc.date.issued 2014-12-31 dc.identifier.issn 0360-5302 dc.identifier.uri http://hdl.handle.net/20.500.11824/227 dc.description.abstract Let H ‚àà C 2(‚ÑùN√ón), H ‚â• 0. The PDE system (Formula presented.) arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ‚àû(u, Œ©) = {norm of matrix}H(Du){norm of matrix}L ‚àû(Œ©) defined on maps u: Œ© ‚äÜ ‚Ñùn ‚Üí ‚ÑùN. (1) first appeared in the author's recent work. The scalar case though has a long history initiated by Aronsson. Herein we study the solutions of (1) with emphasis on the case of n = 2 ‚â§ N with H the Euclidean norm on ‚ÑùN√ón, which we call the "‚àû-Laplacian". By establishing a rigidity theorem for rank-one maps of independent interest, we analyse a phenomenon of separation of the solutions to phases with qualitatively different behaviour. As a corollary, we extend to N ‚â• 2 the Aronsson-Evans-Yu theorem regarding non existence of zeros of {pipe}Du{pipe} and prove a maximum principle. We further characterise all H for which (1) is elliptic and also study the initial value problem for the ODE system arising for n = 1 but with H(¬∑, u, u‚Ä≤) depending on all the arguments. dc.format application/pdf dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.title On the Structure of $\infty$-Harmonic Maps dc.type info:eu-repo/semantics/article en_US dc.identifier.doi 10.1080/03605302.2014.920351 dc.relation.publisherversion http://www.tandfonline.com/doi/abs/10.1080/03605302.2014.920351 dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US dc.journal.title Communications in Partial Differential Equations en_US
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