Stability of quasiconvex hulls and deformations with finitely many gradients

Bernd Kirchheim

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Submission date: 18. May. 2000
Pages: 8
published in: Comptes rendus de l'Académie des Sciences / 1, 332 (2001) 3, p. 289-294 
DOI number (of the published article): 10.1016/S0764-4442(00)01792-4
Bibtex
with the following different title: Deformations with finitely many gradients and stability of quasiconvex hulls
MSC-Numbers: 26B25, 49K24
Keywords and phrases: rank-one and quasiconvexity, differential inclusions, baire category
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Abstract:
We answer a question by Kewei Zhang concerning the existence of sets with stable quasiconvex hulls. As a consequence we confirm a conjecture by John M. Ball about the existence of lipschitz maps using finitely many gradients without any rank-one connection. These functions are obtained using a new argument which unifies the convex integration method and the present Baire category approach to the existence of solutions of partial differential inclusions.