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Convex Variational Problems

Linear, nearly Linear and Anisotropic Growth Conditions

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1818)

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Table of contents (12 chapters)

  1. Front Matter

    Pages N2-X
  2. 1. Introduction

    • Michael Bildhauer
    Pages 1-12
  3. A. Some remarks on relaxation

    • Michael Bildhauer
    Pages 173-183
  4. B. Some density results

    • Michael Bildhauer
    Pages 185-198
  5. D. Notation and conventions

    • Michael Bildhauer
    Pages 205-206
  6. References

    • Michael Bildhauer
    Pages 207-213
  7. Index

    • Michael Bildhauer
    Pages 215-217
  8. Back Matter

    Pages 219-219

About this book

The author emphasizes a non-uniform ellipticity condition as the main approach to regularity theory for solutions of convex variational problems with different types of non-standard growth conditions.

This volume first focuses on elliptic variational problems with linear growth conditions. Here the notion of a "solution" is not obvious and the point of view has to be changed several times in order to get some deeper insight. Then the smoothness properties of solutions to convex anisotropic variational problems with superlinear growth are studied. In spite of the fundamental differences, a non-uniform ellipticity condition serves as the main tool towards a unified view of the regularity theory for both kinds of problems.

Keywords

  • Non-standard growth
  • Smooth function
  • anisotropic growth
  • linear growth
  • minimizers
  • regularity
  • partial differential equations

Bibliographic Information

  • Book Title: Convex Variational Problems

  • Book Subtitle: Linear, nearly Linear and Anisotropic Growth Conditions

  • Authors: Michael Bildhauer

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b12308

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2003

  • Softcover ISBN: 978-3-540-40298-5Published: 20 June 2003

  • eBook ISBN: 978-3-540-44885-3Published: 01 January 2003

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 220

  • Topics: Calculus of Variations and Optimization, Differential Equations

Buying options

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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions