A Study of the Integrability of the Derivatives of the Solutions of the Conjugate (nonlinear) Beltrami Equation

In this article we study degenerate elliptic equations. Using integral representations for the function posessing generalised derivatives we prove theorems of existence of solutions of these equations in the class of quasiconformal mappings in the mean, and in the more general case. We prove higher integrability of the solutions of these equations in the case of the boundary degeneration.

conjugate (nonlinear) Beltrami equation, degenerate elliptic equations, Muckenhoupt’s weight function, weighted Sobolev’s space, embedding theorems, bounded singular operator in weighted space, quasiconformal mappings