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MiS Preprint
16/2007
On the gradient set of Lipschitz maps
Bernd Kirchheim and László Székelyhidi
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 {$\mathbb{R}^{2\times 2}$}. Preprint, MPI-MIS, 2006. we obtain a complete characterization of incompatible sets of gradients for planar maps in terms of rank-one convexity.
