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Elements of Nonlinear Analysis

BuchGebunden
256 Seiten
Englisch
Springererschienen am01.11.2000
The goal of this book is to present some modern aspects of nonlinear analysis. Starting with the basics of the linear theory, we introduce a first type of nonlinear problem that has today invaded the whole mathematical world: variational inequalities.mehr
Verfügbare Formate
BuchGebunden
EUR53,49
BuchKartoniert, Paperback
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Produkt

KlappentextThe goal of this book is to present some modern aspects of nonlinear analysis. Starting with the basics of the linear theory, we introduce a first type of nonlinear problem that has today invaded the whole mathematical world: variational inequalities.
Details
ISBN/GTIN978-3-7643-6406-9
ProduktartBuch
EinbandartGebunden
Verlag
Erscheinungsjahr2000
Erscheinungsdatum01.11.2000
ReiheBirkhäuser Advanced Texts Basler Lehrbücher
Seiten256 Seiten
SpracheEnglisch
Gewicht556 g
IllustrationenVII, 256 p.
Artikel-Nr.10906413

Inhalt/Kritik

Inhaltsverzeichnis
1. Some Physical Motivations.- 1.1. An elementary theory of elasticity.- 1.2. A problem in biology.- 1.3. Exercises.- 2. A Short Background in Functional Analysis.- 2.1. An introduction to distributions.- 2.2. Integration on boundaries.- 2.3. Introduction to Sobolev spaces.- 2.4. Exercises.- 3. Elliptic Linear Problems.- 3.1. The Dirichlet problem.- 3.2. The Lax-Milgram theorem and its applications.- 3.3. Exercises.- 4. Elliptic Variational Inequalities.- 4.1. A generalization of the Lax-Milgram theorem.- 4.2. Some applications.- 4.3. Exercises.- 5. Nonlinear Elliptic Problems.- 5.1. A compactness method.- 5.2. A monotonicity method.- 5.3. A generalization of variational inequalities.- 5.4. Some multivalued problems.- 5.5. Exercises.- 6. A Regularity Theory for Nonlocal Variational Inequalities.- 6.1. Some general results.- 6.2. Applications to second order variational inequalities.- 6.3. Exercises.- 7. Uniqueness and Nonuniqueness Issues.- 7.1. Uniqueness result for local nonlinear problems.- 7.2. Nonuniqueness issues.- 7.3. Exercises.- 8. Finite Element Methods for Elliptic Problems.- 8.1. An abstract setting.- 8.2. Some simple finite elements.- 8.3. Interpolation error.- 8.4. Convergence results.- 8.5. Approximation of nonlinear problems.- 8.6. Exercises.- 9. Minimizers.- 9.1. Introduction.- 9.2. The direct method.- 9.3. Applications.- 9.4. The Euler Equation.- 9.5. Exercises.- 10. Minimizing Sequences.- 10.1. Some model problems.- 10.2. Young measures.- 10.3. Construction of the minimizing sequences.- 10.4. A more elaborate issue.- 10.5. Numerical analysis of oscillations.- 10.6. Exercises.- 11. Linear Parabolic Equations.- 11.1. Introduction.- 11.2. Functional analysis for parabolic problems.- 11.3. The resolution of parabolic problems.- 11.4. Applications.- 11.5.Exercises.- 12. Nonlinear Parabolic Problems.- 12.1. Local problems.- 12.2. Nonlocal problems.- 12.3. Exercises.- 13. Asymptotic Analysis.- 13.1. The case of one stationary point.- 13.2. The case of several stationary points.- 13.3. A nonlinear case.- 13.4. Blow-up.- 13.5. Exercises.mehr
Kritik
"This is a relatively formal book which starts out as a motivational chapter introducing two examples, elasticity and diffusion, of the application of nonlinear analysis. Aimed mainly at graduate students and nonspecialists, the material is then developed in a largely abstract fashion, introducing topics in existence, uniqueness, regularity and approximation for elliptic and parabolic problems." --Aslib Book Guide



"This book covers some of the main aspects of nonlinear analysis. It concentrates on stressing the fundamental ideas instead of elaborating on the intricacies of the more esoteric ones...it encompass[es] many methods of dynamical systems in quite simple and original settings. I recommend this book to anyone interested in the main and essential concepts of nonlinear analysis as well as the relevant methodologies and applications." --Mathematical Reviewsmehr