Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8312Research ArticleA Study of the Integrability of the Derivatives of the Solutions of the Conjugate (nonlinear) Beltrami EquationTerentievaJ VChair of «Theory of the functions»tuv86@mail.ruKuban State University15012013151808092016Copyright © 2013,2013In 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 equationdegenerate elliptic equationsMuckenhoupt’s weight functionweighted Sobolev’s spaceembedding theoremsbounded singular operator in weighted spacequasiconformal mappingsсопряжённое (нелинейное) уравнение Бельтрамивырождающиеся эллиптические уравнениякласс Макенхауптавесовые соболевские пространстватеоремы вложенияограниченные сингулярные операторы в весовых пространствахквазиконформные отображения