Dirichlet-Type Problems for Certain Beltrami Equations

In this paper, we shall be interested in solving Dirichlet-type problems for solutions of certain classes of Beltrami equations, to be called β-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta -$$\end{document}analytic. Orthogonal decomposition of the corresponding Sobolev space as well as the ortho-projections onto the subspaces of theses decompositions are obtained. Analytic representation formulas for the underlying solutions in terms of integral operators are established.