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.
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Communicated by S. Müller
Research supported in part by grants from the Finnish Academy, the U.S. National Science Foundation and the N.Z. Marsden Fund.
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Astala, K., Iwaniec, T. & Martin, G. Deformations of Annuli with Smallest Mean Distortion. Arch Rational Mech Anal 195, 899–921 (2010). https://doi.org/10.1007/s00205-009-0231-z
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DOI: https://doi.org/10.1007/s00205-009-0231-z