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.
|Number of pages||34|
|Journal||Proceedings of the London Mathematical Society|
|Early online date||28 Nov 2017|
|Publication status||Published - 6 Apr 2018|
- 46E35 (secondary)
- 49Q20 (primary)
ASJC Scopus subject areas
FingerprintDive into the research topics of 'Structure and rigidity of functions in BVloc2(R2) with gradients taking only three values'. Together they form a unique fingerprint.
- Department of Mathematical Sciences - Professor
Person: Research & Teaching