

Preprint 16/2007
On the gradient set of Lipschitz maps
Bernd Kirchheim and László Székelyhidi
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Submission date: 12. Feb. 2007
Pages: 16
published in: Journal für die reine und angewandte Mathematik, 625 (2008), p. 215-229
DOI number (of the published article): 10.1515/CRELLE.2008.095
Bibtex
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Abstract:
We prove that the essential range of the gradient of planar Lipschitz maps has a connected
rank-one convex hull. As a corollary, in combination with the results in Faraco, D., and Székelyhidi, Jr., L.:
Tartar's conjecture and localization of the quasiconvex hull in
. Preprint, MPI-MIS, 2006.
we obtain
a complete characterization of incompatible sets of gradients for planar maps in terms of rank-one convexity.