The failure of lower semicontinuity for the linear dilatation

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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.

Original languageEnglish (US)
Pages (from-to)55-61
Number of pages7
JournalBulletin of the London Mathematical Society
Volume30
Issue number1
DOIs
StatePublished - Jan 1998

ASJC Scopus subject areas

  • Mathematics(all)

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