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Stability of quasiconvex hulls and deformations with finitely many gradients
Bernd KirchheimAbstract
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.
- Received:
- 18.05.00
- Published:
- 18.05.00
- MSC Codes:
- 26B25, 49K24
- Keywords:
- rank-one and quasiconvexity, differential inclusions, baire category