Mariano Giaquinta

(Author)

Calculus of Variations II (1996. Corr. 2nd Printing 2004)Hardcover - 1996. Corr. 2nd Printing 2004, 1 March 1996

Calculus of Variations II (1996. Corr. 2nd Printing 2004)
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Part of Series
Grundlehren Der Mathematischen Wissenschaften
Part of Series
Applications of Mathematics,
Part of Series
Grundlehren Der Mathematischen Wissenschaften (Springer Hardcover)
Print Length
655 pages
Language
English
Publisher
Springer
Date Published
1 Mar 1996
ISBN-10
3540579613
ISBN-13
9783540579618

Description

This book describes the classical aspects of the variational calculus which are of interest to analysts, geometers and physicists alike. Volume 1 deals with the for- mal apparatus of the variational calculus and with nonparametric field theory, whereas Volume 2 treats parametric variational problems as weIl as Hamilton- Jacobi theory and the classical theory of partial differential equations of first order. In a subsequent treatise we shall describe developments arising from Hilbert's 19th and 20th problems, especially direct methods and regularity theory. Of the classical variational calculus we have particularly emphasized the often neglected theory of inner variations, i. e. of variations of the independent variables, which is a source of useful information such as monotonicity for- mulas, conformality relations and conservation laws. The combined variation of dependent and independent variables leads to the general conservation laws of Emmy Noether, an important tool in exploiting symmetries. Other parts of this volume deal with Legendre-Jacobi theory and with field theories. In particular we give a detailed presentation of one-dimensional field theory for non para- metric and parametric integrals and its relations to Hamilton-Jacobi theory, geometrieal optics and point mechanics. Moreover we discuss various ways of exploiting the notion of convexity in the calculus of variations, and field theory is certainly the most subtle method to make use of convexity. We also stress the usefulness of the concept of a null Lagrangian which plays an important role in several instances.

Product Details

Authors:
Mariano GiaquintaStefan Hildebrandt
Book Edition:
1996. Corr. 2nd Printing 2004
Book Format:
Hardcover
Country of Origin:
US
Date Published:
1 March 1996
Dimensions:
23.39 x 15.6 x 3.66 cm
ISBN-10:
3540579613
ISBN-13:
9783540579618
Language:
English
Location:
Berlin, Heidelberg
Pages:
655
Publisher:
Weight:
1129.44 gm

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