Article contents
THE FAILURE OF LOWER SEMICONTINUITY FOR THE LINEAR DILATATION
Published online by Cambridge University Press: 01 January 1998
Abstract
Since the very beginning of the multidimensional theory of quasiregular mappings, it has been widely believed that the class of K-quasiregular mappings in ℝn is closed with respect to uniform convergence, where K stands for the linear dilatation. In this note we give a striking example which refutes this belief. The key element of our construction is that the linear dilatation function fails to be rank-one convex in dimensions higher than 2.
- Type
- Research Article
- Information
- Copyright
- © The London Mathematical Society 1998
- 8
- Cited by