A characterisation of infinity-harmonic and p-harmonic maps via affine variations in L-infinity

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dc.contributor.authorKatzourakis, Nikos
dc.date.accessioned2022-03-21T19:24:06Z
dc.date.available2022-03-21T19:24:06Z
dc.date.issued2017-01-26
dc.description.abstractLet u : Ω ⊆ ℝn → ℝN be a smooth map and n, N ∈ ℕ. The ∞-Laplacian is the PDE system ∆∞u ≔ (Du ⊗ Du + |Du|2 [Du]⊥ ⊗ I) : D2u = 0, where [Du]⊥ ≔ ProjR(Du)⊥. This system constitutes the fundamental equation of vectorial Calculus of Variations in L∞, associated with the model functional E∞(u, Ω′) = ∥|Du|2∥L∞(Ω′), Ω′ ⋐ Ω. We show that generalised solutions to the system can be characterised in terms of the functional via a set of designated affine variations. For the scalar case N = 1, we utilise the theory of viscosity solutions by Crandall-Ishii-Lions. For the vectorial case N ≥ 2, we utilise the recently proposed by the author theory of D-solutions. Moreover, we extend the result described above to the p-Laplacian, 1 < p < ∞.
dc.description.departmentMathematics
dc.formatText
dc.format.extent19 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationKatzourakis, N. (2017). A characterisation of infinity-harmonic and p-harmonic maps via affine variations in L-infinity. <i>Electronic Journal of Differential Equations, 2017</i>(29), pp. 1-19.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/15534
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectInfinity-Laplacian
dc.subjectp-Laplacian
dc.subjectGeneralised solutions
dc.subjectViscosity solutions
dc.subjectCalculus of variations in L-infinity
dc.subjectYoung measures
dc.subjectFully nonlinear systems
dc.titleA characterisation of infinity-harmonic and p-harmonic maps via affine variations in L-infinity
dc.typeArticle

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