Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions
著者
書誌事項
Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions
（Lecture notes in mathematics, 1445）
Springer-Verlag, c1990
- : gw
- : us
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注記
Bibliography: p. [115]-120
Includes indexes
内容説明・目次
内容説明
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.
目次
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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