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Structure and rigidity of functions in BV loc 2 ( R 2 ) with gradients taking only three values
Author(s) -
Moser Roger
Publication year - 2018
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms.12094
Subject(s) - mathematics , rigidity (electromagnetism) , pure mathematics , affine transformation , hausdorff space , almost everywhere , mathematical analysis , engineering , structural engineering
Abstract Consider a function u ∈ BV loc 2 ( 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.