n-Harmonic mappings between annuli : the art of integrating free Lagrangians
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Bibliographic Information
n-Harmonic mappings between annuli : the art of integrating free Lagrangians
（Memoirs of the American Mathematical Society, no. 1023）
American Mathematical Society, 2012, c2011
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"July 2012, volume 218, number 1023 (first of 5 numbers)."
Includes bibliographical references (p. 103-105)
Description and Table of Contents
Description
The central theme of this paper is the variational analysis of homeomorphisms $h: {\mathbb X} \overset{\textnormal{\tiny{onto}}}{\longrightarrow} {\mathbb Y}$ between two given domains ${\mathbb X}, {\mathbb Y} \subset {\mathbb R}^n$. The authors look for the extremal mappings in the Sobolev space ${\mathscr W}^{1,n}({\mathbb X},{\mathbb Y})$ which minimize the energy integral ${\mathscr E}_h=\int_{<!-- -->{\mathbb X}} \,|\!|\, Dh(x) \,|\!|\,^n\, \textrm{d}x$. Because of the natural connections with quasiconformal mappings this $n$-harmonic alternative to the classical Dirichlet integral (for planar domains) has drawn the attention of researchers in Geometric Function Theory. Explicit analysis is made here for a pair of concentric spherical annuli where many unexpected phenomena about minimal $n$-harmonic mappings are observed. The underlying integration of nonlinear differential forms, called free Lagrangians, becomes truly a work of art.
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