Nonlinear Functional Analysis and its Applications: II/B: Nonlinear Monotone Operators

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Springer Science & Business Media, 21 nov 2013 - 741 pagine
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.
 

Sommario

CHAPTER 32
840
CHAPTER 33
919
GENERAL THEORY OF DISCRETIZATION METHODS
959
CHAPTER 35
978
CHAPTER 36
997
Appendix
1009
References
1119
List of Symbols
1163

CHAPTER 29
639
Auxiliary Tools and the Convergence of the Galerkin
721
GENERALIZATION TO NONLINEAR
765
Hilbert Space Methods and Linear Elliptic Differential Equations 314
767
CHAPTER 31
816
List of Theorems
1174
List of Schematic Overviews
1182
Index
1189
Copyright

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