Archive for Rational Mechanics and Analysis

, Volume 195, Issue 3, pp 899-921

First online:

Deformations of Annuli with Smallest Mean Distortion

  • K. AstalaAffiliated withDepartment of Mathematics, University of Helsinki
  • , T. IwaniecAffiliated withDepartment of Mathematics, Syracuse University
  • , G. MartinAffiliated withInstitute for Advanced Study, Massey University Email author 

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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.