Abstract: The theory of quasiconformal mappings is the extension of Riemann conformal mappings. It has been widely applied in many mathematic fields since proposed by Ahlfors etal. This paper explores the solvability of a class of quasilinear elliptic equation Dirichlet problem by using conformal mappings, Schauder estimates, barrier function and Schauder fixed point theorem. The novelty of this paper is that our method is based on the priori estimate of linear elliptic equations of two variables.

Key words: quasiconformal mappings; Schauder-s interior estimates; barrier functions; Schauder-s fixed point theorem