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dc.contributor.authorKatzourakis, N.I.
dc.date.accessioned2016-06-13T13:33:49Z
dc.date.available2016-06-13T13:33:49Z
dc.date.issued2014-12-31
dc.identifier.issn0360-5302
dc.identifier.urihttp://hdl.handle.net/20.500.11824/227
dc.description.abstractLet H ∈ C 2(ℝN×n), H ≥ 0. The PDE system (Formula presented.) arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ∞(u, Ω) = {norm of matrix}H(Du){norm of matrix}L ∞(Ω) defined on maps u: Ω ⊆ ℝn → ℝN. (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 ≤ N with H the Euclidean norm on ℝN×n, which we call the "∞-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 ≥ 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′) depending on all the arguments.
dc.formatapplication/pdf
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.titleOn the Structure of $\infty$-Harmonic Maps
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1080/03605302.2014.920351
dc.relation.publisherversionhttp://www.tandfonline.com/doi/abs/10.1080/03605302.2014.920351
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleCommunications in Partial Differential Equationsen_US


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Reconocimiento-NoComercial-CompartirIgual 3.0 España
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