Skip to main content
SpringerLink
Log in

Convex Analysis and Nonlinear Geometric Elliptic Equations

  • Book
  • © 1994

Overview

Authors:
  1. Ilya J. Bakelman
    View author publications

    You can also search for this author in PubMed   Google Scholar

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (8 chapters)

  1. Front Matter

    Pages I-XXI
    Download chapter PDF

  2. Elements of Convex Analysis

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Convex Bodies and Hypersurfaces

      • Ilya J. Bakelman
      Pages 3-53

    3. Mixed Volumes. Minkowski Problem. Selected Global Problems in Geometric Partial Differential Equations

      • Ilya J. Bakelman
      Pages 54-107

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

    1. Front Matter

      Pages 109-111
      Download chapter PDF

    2. Generalized Solutions of N-Dimensional Monge-Ampere Equations

      • Ilya J. Bakelman
      Pages 113-181

    3. Variational Problems and Generalized Elliptic Solutions of Monge-Ampere Equations

      • Ilya J. Bakelman
      Pages 182-203

    4. Non-Compact Problems for Elliptic Solutions of Monge-Ampere Equations

      • Ilya J. Bakelman
      Pages 204-226

    5. Smooth Elliptic Solutions of Monge-Ampere Equations

      • Ilya J. Bakelman
      Pages 226-283

  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
      Download chapter PDF

    2. Geometric Concepts and Methods in Nonlinear Elliptic Euler-Lagrange Equations

      • Ilya J. Bakelman
      Pages 287-339

    3. The Geometric Maximum Principle for General Non-Divergent Quasilinear Elliptic Equations

      • Ilya J. Bakelman
      Pages 339-495

  5. Back Matter

    Pages 497-510
    Download chapter PDF
Back to top

Keywords

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.

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation