$n$-Harmonic Mappings Between Annuli

The Art of Integrating Free Lagrangians

Tadeusz Iwaniec, Jani Onninen (Autoren)

Buch | Softcover

105 Seiten

2012
American Mathematical Society (Verlag)
978-0-8218-5357-3 (ISBN)

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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.

Erscheint lt. Verlag	1.7.2012
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Gewicht	300 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-8218-5357-0 / 0821853570
ISBN-13	978-0-8218-5357-3 / 9780821853573
Zustand	Neuware