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THE FAILURE OF LOWER SEMICONTINUITY FOR THE LINEAR DILATATION

Published online by Cambridge University Press:  01 January 1998

TADEUSZ IWANIEC
TADEUSZ IWANIEC
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA
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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
Bulletin of the London Mathematical Society , Volume 30 , Issue 1 , January 1998 , pp. 55 - 61
Copyright
© The London Mathematical Society 1998

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