On the numerical approximation of vectorial absolute minimisers in L

Nikos Katzourakis, Tristan Pryer

Research output: Contribution to journalArticle

Abstract

Let Ω be an open set. We consider the supremal functional E∞(u,O):=‖Du‖L∞(O),O⊆Ωopen,applied to locally Lipschitz mappings u: Rn⊇ Ω ⟶ RN, where n, N∈ N. This is the model functional of Calculus of Variations in L. The area is developing rapidly, but the vectorial case of N≥ 2 is still poorly understood. Due to the non-local nature of (1), usual minimisers are not truly optimal. The concept of so-called absolute minimisers is the primary contender in the direction of variational concepts. However, these cannot be obtained by direct minimisation and the question of their existence under prescribed boundary data is open when n, N≥ 2. We present numerical experiments aimed at understanding the behaviour of minimisers through a new technique involving p-concentration measures.

Original languageEnglish
Article number51
JournalNonlinear Differential Equations and Applications
Volume27
Issue number6
Early online date10 Oct 2020
DOIs
Publication statusPublished - 1 Dec 2020

Keywords

  • Aronsson equation
  • Calculus of Variations in L
  • Supremal functionals
  • Vectorial absolute minimisers
  • ∞-Laplacian

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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