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On the gradient set of Lipschitz maps

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 [7] we obtain a complete characterization of incompatible sets of gradients for planar maps in terms of rank-one convexity. © 2008 Walter de Gruyter Berlin · New York.
Publication status:
Published

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Publisher copy:
10.1515/CRELLE.2008.095

Authors


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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
Volume:
625
Issue:
625
Pages:
215-229
Publication date:
2008-12-05
DOI:
EISSN:
0075-4102
ISSN:
0075-4102
URN:
uuid:fe5fd5e5-ae13-4c2a-b4f8-5c3263988f57
Source identifiers:
27347
Local pid:
pubs:27347
Language:
English

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