Direct methods in the calculus of variations

Bibliographic Information

Direct methods in the calculus of variations

Enrico Giusti

World Scientific, c2003

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Note

Includes bibliographical references (p. 377-398) and index

Description and Table of Contents

Description

This book provides a comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. While direct methods for the existence of solutions are well known and have been widely used in the last century, the regularity of the minima was always obtained by means of the Euler equation as a part of the general theory of partial differential equations. In this book, using the notion of the quasi-minimum introduced by Giaquinta and the author, the direct methods are extended to the regularity of the minima of functionals in the calculus of variations, and of solutions to partial differential equations. This unified treatment offers a substantial economy in the assumptions, and permits a deeper understanding of the nature of the regularity and singularities of the solutions. The book is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory.

Table of Contents

  • Semi-Classical Theory
  • Integrable Functions
  • Sobolev Spaces
  • Semicontinuity
  • Quasi-Convex Functionals
  • Quasi-Minima
  • Regularity of Quasi-Minima
  • First Derivatives
  • Partial Regularity
  • Higher Derivatives.

by "Nielsen BookData"

Details

  • NCID
    BA61083956
  • ISBN
    • 9812380434
  • LCCN
    2005277642
  • Country Code
    us
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    River Edge, NJ ; Singapore
  • Pages/Volumes
    vii, 403 p.
  • Size
    24 cm
  • Classification
  • Subject Headings
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