Direct Methods in the Calculus of Variat

Direct Methods in the Calculus of Variat
2 031,- 2 031,-
Førpris 2539,- Spar 508,-
Førpris 2539,- Spar 508,-
Format E-Bok
Filformat PDF
Utgivelsesår 2003
Forlag World Scientific Publishing Co
Språk Engelsk
ISBN 9789812795557
Sider 412
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Om Direct Methods in the Calculus of Variat

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.Contents:Semi-Classical TheoryMeasurable FunctionsSobolev SpacesConvexity and SemicontinuityQuasi-Convex FunctionalsQuasi- MinimaHölder ContinuityFirst DerivativesPartial RegularityHigher DerivativesReadership: Graduate students, academics and researchers in the field of analysis and differential equations.Key Features:Unique and original treatment of the known resultsElaborate description of the current and possible future theoretical and experimental investigationThe ab ovo approach is well adapted for the newcomers in the field


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