Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 38, 2013, 91-113

WEIGHTED ESTIMATES FOR BELTRAMI EQUATIONS

Albert Clop and Victor Cruz

Universitat Autònoma de Barcelona, Departament de Matemàtiques
08193 Bellaterra, Barcelona, Catalonia; albertcp 'at' mat.uab.cat

Universidad Tecnológica de la Mixteca, Instituto de Física y Matemáticas
69000 Huajauapan de León, Oaxaca, México; victorcruz 'at' mixteco.utm.mx

Abstract. We obtain a priori estimates in L^p(\omega) for the generalized Beltrami equation, provided that the coefficients are compactly supported VMO functions with the expected ellipticity condition, and the weight \omega lies in the Muckenhoupt class A_p. As an application, we obtain improved regularity for the jacobian of certain quasiconformal mappings.

2010 Mathematics Subject Classification: Primary 30C62, 35J15, 42B37.

Key words: Beltrami equation, quasiconformal mapping, Muckenhoupt weight.

Reference to this article: A. Clop and V. Cruz: Weighted estimates for Beltrami equations. Ann. Acad. Sci. Fenn. Math. 38 (2013), 91-113.

Full document as PDF file

doi:10.5186/aasfm.2013.3818

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