Convex Variational Problems

Linear, Nearly Linear and Anisotropic Growth Conditions

  • Authors
  • Michael Bildhauer

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

Table of contents

  1. Front Matter
    Pages N2-X
  2. Michael Bildhauer
    Pages 1-12
  3. Michael Bildhauer
    Pages 173-183
  4. Michael Bildhauer
    Pages 185-198
  5. Michael Bildhauer
    Pages 205-206
  6. Michael Bildhauer
    Pages 207-213
  7. Michael Bildhauer
    Pages 215-217
  8. Back Matter
    Pages 219-219

About this book

Introduction

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

Bibliographic information

  • DOI https://doi.org/10.1007/b12308
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-40298-5
  • Online ISBN 978-3-540-44885-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book