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  • © 1994

Convex Analysis and Nonlinear Geometric Elliptic Equations

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  • ISBN: 978-3-642-69881-1
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Table of contents (8 chapters)

  1. Front Matter

    Pages I-XXI
  2. Elements of Convex Analysis

    1. Front Matter

      Pages 1-1
    2. Convex Bodies and Hypersurfaces

      • Ilya J. Bakelman
      Pages 3-53
  3. Geometric Theory of Elliptic Solutions of Monge-Ampere Equations

    1. Front Matter

      Pages 109-111
  4. Geometric Methods in Elliptic Equations of Second Order. Applications to Calculus of Variations, Differential Geometry and Applied Mathematics

    1. Front Matter

      Pages 285-285
  5. Back Matter

    Pages 497-510

About this book

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

Buying options

eBook
USD 84.99
Price excludes VAT (USA)
  • ISBN: 978-3-642-69881-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 109.99
Price excludes VAT (USA)