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Structure and rigidity of functions in BVloc2(R2) with gradients taking only three values
OAI: oai:purehost.bath.ac.uk:publications/6a4f2186-0ca7-4802-9d04-f47beafb6941 • DOI: https://doi.org/10.1112/plms.12094
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.