Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions
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Bibliographic Information
Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions
（Lecture notes in mathematics, 1445）
Springer-Verlag, c1990
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Library & Science Information Center, Osaka Prefecture University
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
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Note
Bibliography: p. [115]-120
Includes indexes
Description and Table of Contents
Description
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 which has never been presented in book form. An exposition of the Heinz-Lewy theory requires auxiliary material which can be found in various monographs, but which is presented here, in part because the focus is different, and also because these notes have an introductory character. Self-contained introductions to the regularity theory of elliptic systems, the theory of pseudoanalytic 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.
Table of Contents
Integral criteria for Hoelder continuity.- Regularity for linear elliptic equations and quasilinear systems.- Regularity for Monge-Ampere equations.- Function theory of elliptic equations.- Univalent solutions of binary elliptic systems.- Conformal mappings with respect to a Riemannian metric.- Local behavior of solutions of differential inequalities.- Univalent solutions of Heinz-Lewy type systems.- A priori estimates for Monge-Ampere equations.- Regularity and a priori estimates for locally convex surfaces.
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