Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

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:
18.05.2000
Published:
18.05.2000
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