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On the gradient set of Lipschitz maps
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Bernd Kirchheim
Published/Copyright:
November 18, 2008
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 R2x2, Acta Math., to appear.] we obtain a complete characterization of incompatible sets of gradients for planar maps in terms of rank-one convexity.
Received: 2007-03-23
Revised: 2008-01-14
Published Online: 2008-11-18
Published in Print: 2008-December
© Walter de Gruyter Berlin · New York 2008
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Articles in the same Issue
- On mixing and ergodicity in locally compact motion groups
- Path integrals on manifolds by finite dimensional approximation
- The Schwartz algebra of an affine Hecke algebra
- Adelic amoebas disjoint from open halfspaces
- Generalized Kac-Moody algebras, automorphic forms and Conway's group II
- A Siegel-Weil formula for automorphic characters: Cubic variation of a theme of Snitz
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