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

  • Book
  • © 1990

Overview

Authors:
  1. Friedmar Schulz
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1445)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XV
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  2. Integral criteria for Hölder continuity

    • Friedmar Schulz
    Pages 1-14

  3. Regularity for linear elliptic equations and quasilinear systems

    • Friedmar Schulz
    Pages 15-27

  4. Regularity for Monge—Ampère equations

    • Friedmar Schulz
    Pages 28-38

  5. Function theory of elliptic equations

    • Friedmar Schulz
    Pages 39-52

  6. Univalent solutions of binary elliptic systems

    • Friedmar Schulz
    Pages 53-60

  7. Conformal mappings with respect to a Riemannian metric

    • Friedmar Schulz
    Pages 61-71

  8. Local behavior of solutions of differential inequalities

    • Friedmar Schulz
    Pages 72-84

  9. Univalent solutions of Heinz-Lewy type systems

    • Friedmar Schulz
    Pages 85-93

  10. A priori estimates for Monge—Ampère equations

    • Friedmar Schulz
    Pages 94-105

  11. Regularity and a priori estimates for locally convex surfaces

    • Friedmar Schulz
    Pages 106-114

  12. Back Matter

    Pages 115-123
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Keywords

About this book

These lecture notes have been written as an introduction to the characteristic theory for two-dimensional Monge-Ampère 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.

Bibliographic Information

  • Book Title: Regularity Theory for Quasilinear Elliptic Systems and Monge - Ampere Equations in Two Dimensions

  • Authors: Friedmar Schulz

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0098277

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1990

  • Softcover ISBN: 978-3-540-53103-6Published: 24 October 1990

  • eBook ISBN: 978-3-540-46678-9Published: 08 December 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XVIII, 130

  • Topics: Differential Geometry, Analysis

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