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Convex Analysis and Nonlinear Geometric Elliptic Equations

  • Authors
  • Ilya J. Bakelman

Table of contents

  1. Front Matter
    Pages I-XXI
  2. Elements of Convex Analysis

  3. Geometric Theory of Elliptic Solutions of Monge-Ampere Equations

  4. Geometric Methods in Elliptic Equations of Second Order. Applications to Calculus of Variations, Differential Geometry and Applied Mathematics

  5. Back Matter
    Pages 497-510

About this book

Introduction

Investigations in modem nonlinear analysis rely on ideas, methods and prob­ lems from various fields of mathematics, mechanics, physics and other applied sciences. In the second half of the twentieth century many prominent, ex­ emplary problems in nonlinear analysis were subject to intensive study and examination. The united ideas and methods of differential geometry, topology, differential equations and functional analysis as well as other areas of research in mathematics were successfully applied towards the complete solution of com­ plex problems in nonlinear analysis. It is not possible to encompass in the scope of one book all concepts, ideas, methods and results related to nonlinear analysis. Therefore, we shall restrict ourselves in this monograph to nonlinear elliptic boundary value problems as well as global geometric problems. In order that we may examine these prob­ lems, we are provided with a fundamental vehicle: The theory of convex bodies and hypersurfaces. In this book we systematically present a series of centrally significant results obtained in the second half of the twentieth century up to the present time. Particular attention is given to profound interconnections between various divisions in nonlinear analysis. The theory of convex functions and bodies plays a crucial role because the ellipticity of differential equations is closely connected with the local and global convexity properties of their solutions. Therefore it is necessary to have a sufficiently large amount of material devoted to the theory of convex bodies and functions and their connections with partial differential equations.

Keywords

Convex analysis Differentialgleichungen zweiter Ordnung Monge-ampere equations calculus curvature differential equation eliptic partial differential equations maximum nicht-lineare Monge-Ampere Gleichungen nonlinear

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-69881-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-69883-5
  • Online ISBN 978-3-642-69881-1
  • Buy this book on publisher's site