Structure and rigidity of functions in BVloc2(R2) with gradients taking only three values

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Abstract

Consider a function u ∈ BV 2 loc(R 2 such that ∇u takes values in a fixed set of three vectors almost everywhere. This condition implies that u is piecewise affine away from a closed set of vanishing one-dimensional Hausdorff measure. Furthermore, there is some rigidity in the sense that away from the exceptional set, small perturbations of u will result only in controllable changes of the structure.

Original languageEnglish
Pages (from-to)813-846
Number of pages34
JournalProceedings of the London Mathematical Society
Volume116
Issue number4
Early online date28 Nov 2017
DOIs
Publication statusPublished - 6 Apr 2018

Keywords

  • 46E35 (secondary)
  • 49Q20 (primary)

ASJC Scopus subject areas

  • Mathematics(all)

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