Weighted estimates for Beltrami equations

2011/12/23 by Albert Clop, Clop, Albert, Víctor Cruz +1 · 1 citation
Mathematics · #30C62 #35J15 #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #math.AP #math.CV #msc:30C62 #msc:35J15

paper · pdf · doi:10.48550/arxiv.1112.5573

25 pages

arxiv created 2011/12/23 · arxiv updated 2011/12/26

Abstract

We obtain a priori estimates in L^p(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 A_p. As an application, we obtain improved regularity for the jacobian of certain quasiconformal mappings.

Cited by

• Fractional weighted Sobolev spaces associated to the Riesz fractional gradient

Related

• On Beltrami equations and Hoelder regularity
• Distributional solutions of the Beltrami equation
• On planar Beltrami equations and Hoelder regularity
• Beltrami equations with coefficient in the Sobolev space W^1,p
• Heating of the Ahlfors-Beurling operator: weakly quasiregular maps on the plane are quasiregular