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Author:   Michel Chipot
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   2002 ed.
Dimensions:   Width: 15.50cm , Height: 1.20cm , Length: 23.50cm
Weight:   1.000kg
ISBN:  

9783764366469

ISBN 10:   376436646
Pages:   181
Publication Date:   01 December 2001
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Introduction to Linear Elliptic Problems.- 1.1. The Lax—Milgram theorem.- 1.2. Elementary notions on Sobolev spaces.- 1.3. Applications to linear elliptic problems.- 2. Some Model Techniques.- 2.1. The case of lateral Dirichlet boundary conditions on a rectangle.- 2.2. The case of lateral Neumann boundary conditions on a rectangle.- 2.3. The case of lateral Dirichlet boundary conditions revisited.- 2.4. A different point of view.- 3. A General Asymptotic Theory for Linear Elliptic Problems.- 3.1. A general convergence result in H1 (S24,).- 3.2. A sharper rate of convergence.- 3.3. Convergence in higher Sobolev spaces.- 4. Nonlinear Elliptic Problems.- 4.1. Variational inequalities.- 4.2. Quasilinear elliptic problems.- 4.3. Strongly nonlinear problems.- 5. Asymptotic Behaviour of some Nonlinear Elliptic Problems.- 5.1. The case of variational inequalities.- 5.2. The case of quasilinear problems.- 6. Elliptic Systems.- 6.1. Some inequalities.- 6.2. Existence results for linear elliptic systems.- 6.3. Nonlinear elliptic systems.- 7. Asymptotic Behaviour of Elliptic Systems.- 7.1. The case of linear elliptic systems satisfying the Legendre condition.- 7.2. The system of elasticity.- 8. Parabolic Equations.- 8.1. Functional spaces for parabolic problems.- 8.2. Linear parabolic problems.- 8.3. Nonlinear parabolic problems.- 9. Asymptotic Behaviour of Parabolic Problems.- 9.1. The linear case.- 9.2. A nonlinear case.- Concluding Remark.

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