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The Failure of Lower Semicontinuity For The Linear Dilatation
Author(s) -
Iwaniec Tadeusz
Publication year - 1998
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609397003299
Subject(s) - mathematics , rank (graph theory) , regular polygon , class (philosophy) , mathematics subject classification , convergence (economics) , convex function , pure mathematics , function (biology) , element (criminal law) , combinatorics , geometry , law , artificial intelligence , evolutionary biology , computer science , political science , economics , biology , economic growth
Since the very beginning of the multidimensional theory of quasiregular mappings, it has been widely believed that the class of K ‐quasiregular mappings in R n 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 indimensions higher than 2. 1991 Mathematics Subject Classication 30C60, 30Cxx.