A planar bi-Lipschitz extension theorem

Journal article
(Original article)

Publication Details

Author(s): Pratelli A, Daneri S
Journal: Advances in Calculus of Variations
Publication year: 2015
Volume: 8
Journal issue: 3
Pages range: 221-266
ISSN: 1864-8266


We prove that, given a planar bi-Lipschitz map u defined on the boundary of the unit square, it is possible to extend it to a function v of the whole square, in such a way that v is still bi-Lipschitz. In particular, denoting by L and L the bi-Lipschitz constants of u and v, with our construction one has L ≤ CL4 (C being an explicit geometric constant). The same result was proved in 1980 by Tukia (see [Ann. Acad. Sci. Fenn. Ser. A I Math. 5 (1980), no. 1, 49-72]), using a completely different argument, but without any estimate on the constant L. In particular, the function v can be taken either smooth or (countably) piecewise affine.

FAU Authors / FAU Editors

Daneri, Sara Prof. Dr.
Juniorprofessur für Analysis
Pratelli, Aldo Prof.
Lehrstuhl für Mathematik

How to cite

Pratelli, A., & Daneri, S. (2015). A planar bi-Lipschitz extension theorem. Advances in Calculus of Variations, 8(3), 221-266. https://dx.doi.org/10.1515/acv-2012-0013

Pratelli, Aldo, and Sara Daneri. "A planar bi-Lipschitz extension theorem." Advances in Calculus of Variations 8.3 (2015): 221-266.


Last updated on 2018-07-10 at 21:53