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ArticleOriginal scientific text

Title

Quasiconformal mappings and Sobolev spaces

Authors 1, 2, 3

Affiliations

  1. University of Jyväskylä, Department of Mathematics, P.O. Box 35, Fin-40351 Jyväskylä, Finland
  2. Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
  3. Permanent address: Department of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland

Abstract

We examine how Poincaré change under quasiconformal maps between appropriate metric spaces having the same Hausdorff dimension. We also show that for many metric spaces the Sobolev functions can be identified with functions satisfying Poincaré, and this allows us to extend to the metric space setting the fact that quasiconformal maps from ℝQ onto ℝQ preserve the Sobolev space L1,Q(ℝQ).

Bibliography

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Studia Mathematica
1998/131/1
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Pages:
1-17
Main language of publication
English
Received
1997-04-01
Published
1998
Exact and natural sciences