The Degenerate Quasicomformal Global Homeomorphism and Two Dimensional Singular Integral Equations

Abstract:

      Suppose that D is a simply connected region whose boundary Г∈C_a¹（０＜a≤１）,the complex function ｑ（ｚ）∈C_a¹ and |ｑ（ｚ）|≤１, the strict form may only be hold for z∈Γ, and equality ｑ（ｚ（ｔ）)ｚ′（ｔ）/ｚ′（ｔ）+1|_z∈Г＝０ may hold only at finite points. In this paper global homeomorphism solutions of a Beltrami equation with the complex dilation q(z) satisfy above conditions and solutions of a kind of two dimensional singular integral equations with the coefficient q(z) were btained.