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Author:   Michel Chipot
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   2000 ed.
Dimensions:   Width: 15.50cm , Height: 1.50cm , Length: 23.50cm
Weight:   1.220kg
ISBN:  

9783764364069

ISBN 10:   3764364068
Pages:   256
Publication Date:   01 November 2000
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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.

Reviews

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 <p> 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 onesa ]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 Reviews

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