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
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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.