Structure and rigidity of functions in      BV     loc    2    (   R  2   )     with gradients taking only three values | Zendy

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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

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.

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