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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.

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