Pure & Applied Mathematics S.
1 total work
The primary aim of this text is to provide an explanation of those first order elliptic systems of partial differentiation equations in the plane whose solutions consist of the composition of an analytic function with a quasiconformal mapping. The text begins with an introductory chapter which covers necessary results on generalized derivatives, singular integral operators and other areas of analysis and measure theory. Explanations are then provided for such topics as the Bers-Nirenberg representation theorem, fundamental solutions, additional representation formulae, asymptotic developments in zeros and poles, generalized Cauchy, Schwarz and Poisson formulae, jump relations for generalized Cauchy integrals and variational methods for Schlicht solutions.