bokomslag $n$-Harmonic Mappings between Annuli
Vetenskap & teknik

$n$-Harmonic Mappings between Annuli

Tadeusz Iwaniec Jani Onninen

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  • 105 sidor
  • 2012
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.
  • Författare: Tadeusz Iwaniec, Jani Onninen
  • Format: Pocket/Paperback
  • ISBN: 9780821853573
  • Språk: Engelska
  • Antal sidor: 105
  • Utgivningsdatum: 2012-06-30
  • Förlag: American Mathematical Society