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

Roger Moser

doi:10.1112/plms.12094

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

Roger Moser

Department of Mathematical Sciences

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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 language	English
Pages (from-to)	813-846
Number of pages	34
Journal	Proceedings of the London Mathematical Society
Volume	116
Issue number	4
Early online date	28 Nov 2017
DOIs	https://doi.org/10.1112/plms.12094
Publication status	Published - 6 Apr 2018

Keywords

46E35 (secondary)
49Q20 (primary)

ASJC Scopus subject areas

Mathematics(all)

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10.1112/plms.12094

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This is a pre-copyedited, author-produced version of an article accepted for publication in Proceedings of the London Mathematical Society following peer review. The version of record: Moser, R. (2018). Structure and rigidity of functions in BV2loc(R2) with gradients taking only 3 values. Proceedings of the London Mathematical Society, 116(3), 813-846, is available online at: https://doi.org/10.1112/plms.12094.
Accepted author manuscript, 489 KB

Cite this

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

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Roger Moser

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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Roger Moser

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