Article
Licensed
Unlicensed
Requires Authentication
Rank-(n – 1) convexity and quasiconvexity for divergence free fields
Published/Copyright:
April 12, 2010
Abstract
We prove that rank-(n – 1) convexity does not imply quasiconvexity with respect to divergence free fields (so-called S-quasiconvexity) in 
for m > n, by adapting the well-known Šverák's counterexample to the solenoidal setting. On the other hand, we also remark that rank-(n – 1) convexity and S-quasiconvexity turn out to be equivalent in the space of n × n diagonal matrices.
Received: 2009-06-22
Revised: 2010-02-04
Accepted: 2010-02-01
Published Online: 2010-04-12
Published in Print: 2010-July
© de Gruyter 2010
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- A variational approach to uniqueness of ground states for certain quasilinear PDEs
- A new proof of the Hölder continuity of solutions to p-Laplace type parabolic equations
- Rank-(n – 1) convexity and quasiconvexity for divergence free fields
- Nonlocal character of the reduced theory of thin films with higher order perturbations
- The Gibbs–Thomson relation for non homogeneous anisotropic phase transitions
Articles in the same Issue
- A variational approach to uniqueness of ground states for certain quasilinear PDEs
- A new proof of the Hölder continuity of solutions to p-Laplace type parabolic equations
- Rank-(n – 1) convexity and quasiconvexity for divergence free fields
- Nonlocal character of the reduced theory of thin films with higher order perturbations
- The Gibbs–Thomson relation for non homogeneous anisotropic phase transitions
