Direct Methods in the Calculus of Variations (Hardcover) (ISBN-13: 9789812380432)

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.

Author: Enrico Giusti
ISBN-10: 9812380434
ISBN-13: 9789812380432
Publisher: World Scientific Publishing Company
Language: English
Published: 01/24/2003
Pages: 412
Format: Hardcover
Weight: 1.58lbs
Size: 9.48h x 6.28w x 1.00d