Nonlinear Functional Analysis and Its Applications, Part 2 A

Linear Monotone Operators

Eberhard Zeidler

468 pages, parution le 01/07/1999

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Résumé

This is the second of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self -contained and accessible to the nonspecialist. Part II concerns the theory of monotone operators. It is divided into two subvolumes, II/A and II/B, which form a unit. The present Part II/A is devoted to linear monotone operators. It serves as an elementary introduction to the modern functional analytic treatment of variational problems, integral equations, and partial differential equations of elliptic, parabolic and hyperbolic type. This book also represents an introduction to numerical functional analysis with applications to the Ritz method along with the method of finite elements, the Galerkin methods, and the difference method. Many exercises complement the text.

The theory of monotone operators is closely related to Hilbert's rigorous justification of the Dirichlet principle, and to the 19th and 20th problems of Hilbert which he formulated in his famous Paris lecture in 1900, and which strongly influenced the development of analysis in the twentieth century.

Contents

Preface to Part II/A

Introduction to the Subject

Chapter 18 Variational Problems, the Ritz Method, and the Idea of Orthogonality
Chapter 19 The Galerkin Method for Differential and Integral Equations, the Friedrichs Extension, and the Idea of Self-Adjointness
Chapter 20 Difference Methods and Stability

Linear Monotone Problems

Chapter 21 Auxiliary Tools and the Convergence of the Galerkin Method for Linear Operator Equations
Chapter 22 Hilbert Space Methods and Linear Elliptic Differential Equations
Chapter 23 Hilbert Space Methods and Linear Parabolic Differential Equations
Chapter 24 Hilbert Space Methods and Linear Hyperbolic Differential Equations

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Eberhard Zeidler
Parution	01/07/1999
Nb. de pages	468
Format	16 x 24
Couverture	Relié
Poids	847g
Intérieur	Noir et Blanc
EAN13	9780387968025
ISBN13	978-3-540-96802-3