A planar bi-Lipschitz extension theorem

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autorinnen und Autoren: Pratelli A, Daneri S
Zeitschrift: Advances in Calculus of Variations
Jahr der Veröffentlichung: 2015
Band: 8
Heftnummer: 3
Seitenbereich: 221-266
ISSN: 1864-8266


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.



FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

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


Zitierweisen

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.

BibTeX: 

Zuletzt aktualisiert 2018-07-10 um 21:53