Beltrami equations with coefficient in the Sobolev space W1,p
Clop, Albert (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Faraco, D. (Universidad Autónoma de Madrid. Departamento de Matemáticas)
Mateu Bennassar, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Orobitg i Huguet, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Zhong, X. (University of Jyväskylä. Department of Mathematics and Statistics)

Date:	2009
Abstract:	We study the removable singularities for solutions to the Beltrami equation ∂f = µ ∂f, where µ is a bounded function, kµk∞ ≤ K−1 K+1 < 1, and such that µ ∈ W1,p for some p ≤ 2. Our results are based on an extended version of the well known Weyl's lemma, asserting that distributional solutions are actually true solutions. Our main result is that quasiconformal mappings with compactly supported Beltrami coefficient µ ∈ W1,p, 2K2 K2+1 < p ≤ 2, preserve compact sets of σ-finite length and vanishing analytic capacity, even though they need not be bilipschitz.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Quasiconformal ; Hausdorff measure ; Removability
Published in:	Publicacions matemàtiques, V. 53 n. 1 (2009) p. 197-230, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/140676
DOI: 10.5565/PUBLMAT_53109_09

34 p, 317.6 KB

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