Deformations of annuli with smallest mean distortion

K. Astala; T. Iwaniec; G. Martin

doi:10.1007/s00205-009-0231-z

Deformations of annuli with smallest mean distortion

K. Astala, T. Iwaniec, G. Martin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

55 Scopus citations

Abstract

We determine the extremal mappings with smallest mean distortion for mappings of annuli. As a corollary, we find that the Nitsche harmonic maps are Dirichlet energy minimizers among all homeomorphisms h: A(r, R) → A(r^′, R^′). However, outside the Nitsche range of the modulus of the annuli, within the class of homeomorphisms, no such energy minimizers exist. In this case we identify the BV-limits of minimizers.

Original language	English (US)
Pages (from-to)	899-921
Number of pages	23
Journal	Archive for Rational Mechanics and Analysis
Volume	195
Issue number	3
DOIs	https://doi.org/10.1007/s00205-009-0231-z
State	Published - Mar 2010

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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AB - We determine the extremal mappings with smallest mean distortion for mappings of annuli. As a corollary, we find that the Nitsche harmonic maps are Dirichlet energy minimizers among all homeomorphisms h: A(r, R) → A(r′, R′). However, outside the Nitsche range of the modulus of the annuli, within the class of homeomorphisms, no such energy minimizers exist. In this case we identify the BV-limits of minimizers.

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Deformations of annuli with smallest mean distortion

Abstract

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