Archive for Rational Mechanics and Analysis

, Volume 195, Issue 3, pp 899–921

Deformations of Annuli with Smallest Mean Distortion

Article

DOI: 10.1007/s00205-009-0231-z

Cite this article as:
Astala, K., Iwaniec, T. & Martin, G. Arch Rational Mech Anal (2010) 195: 899. doi:10.1007/s00205-009-0231-z

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 \({h:{{\mathbb A}}(r, R) \to {{\mathbb A}}(r', R')}\) . 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.

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HelsinkiHelsinkiFinland
  2. 2.Department of MathematicsSyracuse UniversitySyracuseUSA
  3. 3.Institute for Advanced StudyMassey UniversityPalmerston NorthNew Zealand