On the numerical approximation of ∞ -harmonic mappings

Nikos Katzourakis, Tristan Pryer

Research output: Contribution to journalArticlepeer-review

16 Citations (SciVal)

Abstract

A map u: Ω ⊆ Rn⟶ ℝN, is said to be ∞-harmonic if it satisfies (Formula Presented.). The system (1) is the model of vector-valued Calculus of Variations in L and arises as the “Euler-Lagrange” equation in relation to the supremal functional E∞(u, Ω) := ǁDuǁL(Ω). In this work we provide numerical approximations of solutions to the Dirichlet problem when n= 2 and in the vector valued case of N= 2 , 3 for certain carefully selected boundary data on the unit square. Our experiments demonstrate interesting and unexpected phenomena occurring in the vector valued case and provide insights on the structure of general solutions and the natural separation to phases they present.

Original languageEnglish
Article number61
JournalNonlinear Differential Equations and Applications
Volume23
Issue number6
DOIs
Publication statusPublished - 1 Dec 2016

Keywords

  • Interfaces
  • Phase separation
  • Vector-valued Calculus of Variations in L
  • ∞-Laplacian

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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