$n$-Harmonic Mappings between Annuli: The Art of Integrating Free Lagrangians
Jan 2012 · American Mathematical Soc.
Ebook
105
Pages
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About this ebook
The central theme of this paper is the variational analysis of homeomorphisms h : h:X onto Y between two given domains X,Y⊂Rn. We look for the extremal mappings in the Sobolev space W1,n(X,Y) which minimize the energy integral Eh=∫X||Dh(x)||n dx. Because of the natural connections with quasiconformal mappings this n 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 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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