$n$-Harmonic Mappings between Annuli (eBook)

Tadeusz Iwaniec (Autor)

eBook Download: PDF

2012
105 Seiten
American Mathematical Society (Verlag)
978-0-8218-9008-0 (ISBN)

Infos

The central theme of this paper is the variational analysis of homeomorphisms $h: {/mathbb X} /overset{/text{onto}}{/longrightarrow} {/mathbb Y}$ 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 ${/mathscr E}_h=/int_{{/mathbb X}} / Dh(x) /^n/, /mathrm{d}x/,.$ 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.

Produkt-Details

• Erscheint lt. Verlag: 6.5.2012
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 0-8218-9008-5 / 0821890085
• ISBN-13: 978-0-8218-9008-0 / 9780821890080