Nonlinear Functional Analysis and Its Applications: II/ A: Linear Monotone OperatorsSpringer Science & Business Media, 6 dic 2012 - 467 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
1 | |
Variational Problems the Ritz Method | 15 |
STATIONARY PROBLEMS 469 | 25 |
CHAPTER | 30 |
Pseudomonotone Operators and QuasiLinear Elliptic | 42 |
References 1119 | 55 |
the Main Theorem on Linear Monotone Operators | 64 |
18 13 | 71 |
CHAPTER 20 | 192 |
LINEAR MONOTONE PROBLEMS | 225 |
List of Schematic Overviews 1182 | 276 |
CHAPTER 22 | 314 |
CHAPTER 28 | 342 |
CHAPTER 23 | 402 |
CHAPTER 24 | 452 |
CHAPTER 19 | 101 |
Altre edizioni - Visualizza tutto
Nonlinear Functional Analysis and its Applications: II/B: Nonlinear Monotone ... E. Zeidler Anteprima limitata - 2013 |
Nonlinear Functional Analysis and Its Applications: II/ A: Linear Monotone ... E. Zeidler Anteprima limitata - 1989 |
Nonlinear Functional Analysis and Its Applications: II/ A: Linear Monotone ... E. Zeidler Anteprima non disponibile - 1990 |
Parole e frasi comuni
approximation boundary condition boundary value problem bounded region C¹(G calculus Cauchy sequence Chapter classical solution compact consider const constant convergence convex Corollary corresponding D(AF definition denote dense derivatives difference equation difference method Dirichlet principle eigenvalue problem elliptic differential equations embedding energetic space equivalent error estimates example exists finite elements Friedrichs extension Galerkin method graph closed Hence Hilbert Hölder inequality implies integral equations L₂(G Lemma Let G linear and continuous linear operator mathematics minimum problem monotone operators nonlinear norm obtain operator equation orthogonal partial differential equations proof of Theorem real H-space region in RN resp Riesz Ritz method scalar product Section self-adjoint operators semigroup set in RN Sobolev spaces strongly monotone subspace Suppose symmetric theory of monotone u₁ unique solution variational problem w₁ W¹(G W₂ yields