The failure of lower semicontinuity for the linear dilatation

Tadeusz Iwaniec

doi:10.1112/S0024609397003299

The failure of lower semicontinuity for the linear dilatation

Tadeusz Iwaniec

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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.

Original language	English (US)
Pages (from-to)	55-61
Number of pages	7
Journal	Bulletin of the London Mathematical Society
Volume	30
Issue number	1
DOIs	https://doi.org/10.1112/S0024609397003299
State	Published - Jan 1998

ASJC Scopus subject areas

General Mathematics

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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.",

author = "Tadeusz Iwaniec",

note = "Funding Information: Received 21 May 1996; revised 5 November 1996. 1991 Mathematics Subject Classification 30C60, 30Cxx. Research supported by NSF Grant DMS-97 06611.",

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N2 - 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.

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The failure of lower semicontinuity for the linear dilatation

Abstract

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