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MiS Preprint

Stability of quasiconvex hulls and deformations with finitely many gradients

Bernd Kirchheim


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.

May 18, 2000
May 18, 2000
MSC Codes:
26B25, 49K24
rank-one and quasiconvexity, differential inclusions, baire category

Related publications

2001 Repository Open Access
Bernd Kirchheim

Deformations with finitely many gradients and stability of quasiconvex hulls

In: Comptes rendus de l'Académie des Sciences / 1, 332 (2001) 3, pp. 289-294