Deformations with finitely many gradients and stability of quasiconvex hulls

Journal article

We confirm a conjecture by J.M. Ball and R.D. James about the existence of Lipschitz maps using finitely many gradients without any rank-one connection. For this purpose, we derive a new stability result for quasiconvex hulls which answers a question by Kewei Zhang. The final construction of the functions is based on a new argument which reduces the existence of solutions of partial differential inclusions ∇ f ∈ K to a very natural stability property. In this way our argument unifies and explains the power of both the convex integration method and the present Baire category approach to such existence questions. © 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.

Authors: Kirchheim, B

• Journal: Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
• Volume: 332
• Issue: 3
• Pages: 289-294
• Publication date: 2001-02-01
• DOI: 10.1016/S0764-4442(00)01792-4
• ISSN: 0764-4442
• Language: English