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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
34/2000

Stability of quasiconvex hulls and deformations with finitely many gradients

Bernd Kirchheim

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.

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

Related publications

inJournal
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