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ℓ Goes to Plus Infinity

Many physical problems are meaningfully formulated in a cylindrical domain. When the size of the cylinder goes to infinity, the solutions, under certain symmetry conditions, are expected to be identical in every cross-section of the domain. The proof of this, however, is sometimes difficult and almo...

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Bibliographic Details
Main Author: Chipot, Michel
Format: eBook
Language:English
Published: Basel Birkhäuser 2002, 2002
Edition:1st ed. 2002
Series:Birkhäuser Advanced Texts Basler Lehrbücher
Subjects:
Differential Equations
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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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