A planar bi-Lipschitz extension theorem

Pratelli A, Daneri S (2015)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2015

Journal

Advances in Calculus of Variations

Book Volume: 8

Pages Range: 221-266

Journal Issue: 3

DOI: 10.1515/acv-2012-0013

Abstract

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.

Authors with CRIS profile

Aldo Pratelli Lehrstuhl für Analysis Sara Daneri Juniorprofessur für Analysis

How to cite

APA:

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

MLA:

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

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