Direct Methods In The Calculus Of Variations (Hardcover)

Enrico Giusti

ISBN 10: 9812380434 / ISBN 13: 9789812380432

Published by World Scientific Publishing Co Pte Ltd, Singapore, 2003

About this Item

Hardcover. 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. A self-contained 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. The work only requires a knowledge of the elements of Lebesgue integration theory. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9789812380432

Bibliographic Details

• Title: Direct Methods In The Calculus Of Variations (Hardcover)
• Publisher: World Scientific Publishing Co Pte Ltd, Singapore
• Publication Date: 2003
• Language: English
• ISBN 10: 9812380434
• ISBN 13: 9789812380432
• Binding: Hardcover
• Condition: new

About this title

Synopsis

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.

Review

.,." complemented with detailed historical notes and interesting results which may be difficult to find elsewhere.?