Document Type

Article

Date

2-4-2011

Embargo Period

11-11-2011

Disciplines

Mathematics

Description/Abstract

The central theme of this paper is the variational analysis of homeomorphisms 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 =ZX ||Dh(x) ||n dx 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.

Additional Information

This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/1102.0959

Source

Harvested from arXiv.org

Included in

Mathematics Commons

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