Direct Methods In The Calculus Of Variations

Enrico Giusti (Univ Di Firenze, Italy)

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Hardback

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English

World Scientific Publishing Co Pte Ltd
24 January 2003

Calculus & mathematical analysis; Calculus of variations

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 were widely-used in the 20th 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 work, 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 volume is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory.

By: Enrico Giusti (Univ Di Firenze Italy)
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
Dimensions: Height: 230mm, Width: 160mm, Spine: 25mm
Weight: 717g
ISBN: 9789812380432
ISBN 10: 9812380434
Pages: 412
Publication Date: 24 January 2003
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Active