Regularity Theory for Quasilinear Elliptic Systems and Monge - Ampere Equations in Two Dimensions

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These lecture notes have been written as an introduction to the characteristic theory for two-dimensional Monge-Ampere equations, a theory largely developed by H.Lewy and E.Heinz. Self-contained introductions to the regularity theory of elliptic systems, the theory of pseudo-analytic functions and the theory of conformal mappings are included. These notes grew out of a seminar given at the University of Kentucky in the fall of 1988 and are intended for graduate students and researchers interested in this area.