Beltrami equations with coefficient in the Sobolev space W1.p

• Autores: Albert Clop, Daniel Faraco Hurtado, Joan Mateu Bennassar, Joan Orobitg i Huguet, Xiao Zhong
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 53, Nº 1, 2009, págs. 197-230
• Idioma: inglés
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• Resumen

  • We study the removable singularities for solutions to the Beltrami equation @f = �Ê @f, where �Ê is a bounded function, k�Êk1 . K.1 K+1 < 1, and such that �Ê �¸ W1,p for some p . 2. Our results are based on an extended version of the well known Weyl�fs lemma, asserting that distributional solutions are actually true solutions. Our main result is that quasiconformal mappings with compactly supported Beltrami coefficient �Ê �¸ W1,p, 2K2 K2+1 < p . 2, preserve compact sets of -finite length and vanishing analytic capacity, even though they need not be bilipschitz.