n-Harmonic Mappings Between Annuli
By Tadeusz Iwaniec, Jani Onninen. 2011
66 citations recorded by the source corpus.
The central theme of this paper is the variational analysis of homeomorphisms $h\colon \mathbb X \onto \mathbb Y$ between two given domains $\mathbb X, \mathbb Y \subset \mathbb R^n$. We look for the extremal mappings in the Sobolev space $\mathscr W^{1,n}(\mathbb X,\mathbb Y)$ which minimize the energy integral \[ \mathscr E_h=\int_{\mathbb X} ||Dh(x)||^n dx. \] 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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/17b7164dbb797eaaaf071da4d687aad12cb40465
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Existence of energy-minimal diffeomorphisms between doubly connected domains (2010, background): “tration of matter [4, 38]. An energy-minimal diffeomorphism may fail to exist when a minimizing sequence collapses, at least partially, onto the boundaryof Ω∗. Thisphenomenon was observed in the papers[2, 18] for a pair of circular annuli. A related phenomenon occurs in free boundary problems for min”