Weighted estimates for Beltrami equations

Albert Clop; Victor Cruz

doi:https://doi.org/10.5186/aasfm.2013.3818

Weighted estimates for Beltrami equations

Albert Clop, Victor Cruz

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

30 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	91-113
Journal	Annales Academiae Scientiarum Fennicae Mathematica
Volume	38
DOIs	https://doi.org/10.5186/aasfm.2013.3818
Publication status	Published - 16 May 2013

Keywords

Beltrami equation
Muckenhoupt weight.
quasiconformal mapping

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title = "Weighted estimates for Beltrami equations",

abstract = "We obtain a priori estimates in Lp(ω) for the generalized Beltrami equation, provided that the coefficients are compactly supported VMO functions with the expected ellipticity condition, and the weight ω lies in the Muckenhoupt class Ap. As an application, we obtain improved regularity for the jacobian of certain quasiconformal mappings.",

keywords = "Beltrami equation, Muckenhoupt weight., quasiconformal mapping",

author = "Albert Clop and Victor Cruz",

year = "2013",

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T1 - Weighted estimates for Beltrami equations

AU - Clop, Albert

AU - Cruz, Victor

PY - 2013/5/16

Y1 - 2013/5/16

N2 - We obtain a priori estimates in Lp(ω) for the generalized Beltrami equation, provided that the coefficients are compactly supported VMO functions with the expected ellipticity condition, and the weight ω lies in the Muckenhoupt class Ap. As an application, we obtain improved regularity for the jacobian of certain quasiconformal mappings.

AB - We obtain a priori estimates in Lp(ω) for the generalized Beltrami equation, provided that the coefficients are compactly supported VMO functions with the expected ellipticity condition, and the weight ω lies in the Muckenhoupt class Ap. As an application, we obtain improved regularity for the jacobian of certain quasiconformal mappings.

KW - Beltrami equation

KW - Muckenhoupt weight.

KW - quasiconformal mapping

U2 - https://doi.org/10.5186/aasfm.2013.3818

DO - https://doi.org/10.5186/aasfm.2013.3818

M3 - Article

VL - 38

SP - 91

EP - 113

ER -