Regularity of $$\log (\partial \phi )$$ log ( ∂ ϕ ) for the Solutions of Beltrami Equations with Coefficient in the Sobolev Space $$W^{1,p}_c({\mathbb {C}})$$ W c 1 , p ( C )

In this paper, we study the regularity of $$\log (\partial \phi )$$ when $$\phi $$ is the principal solution of the homogeneous Beltrami equation and the coefficient $$\mu $$ has compact support and is in the Sobolev space $$W^{1,p}_c({\mathbb {C}})$$ with $$1

Keywords:

• Beltrami equation
• Combinatorics
• Sobolev space
• Homogeneous
• Mathematics

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