Elliptic equations : an introductory course

Bibliographic Information

Elliptic equations : an introductory course

Michel Chipot

(Birkhäuser advanced texts : Basler Lehrbücher / edited by Herbert Amann, Hanspeter Kraft)

Birkhäuser, c2009

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Includes bibliographical references and index

Description and Table of Contents

Description

The aim of this book is to introduce the reader to different topics of the theory of elliptic partial differential equations by avoiding technicalities and refinements. Apart from the basic theory of equations in divergence form it includes subjects such as singular perturbation problems, homogenization, computations, asymptotic behaviour of problems in cylinders, elliptic systems, nonlinear problems, regularity theory, Navier-Stokes system, p-Laplace equation. Just a minimum on Sobolev spaces has been introduced, and work or integration on the boundary has been carefully avoided to keep the reader's attention on the beauty and variety of these issues. The chapters are relatively independent of each other and can be read or taught separately. Numerous results presented here are original and have not been published elsewhere. The book will be of interest to graduate students and faculty members specializing in partial differential equations.

Table of Contents

Preface.- I. Basic techniques.- 1. Hilbert space techniques.- 2. A survey of essential analysis.- 3. Weak formulation of elliptic problems.- 4. Elliptic problems in divergence form.- 5. Singular perturbation problems.- 6. Problems in large cylinders.- 7. Periodic problems.- 8. Homogenization.- 9. Eigenvalues.- 10. Numerical computations.- II. More advanced theory.- 11. Nonlinear problems.- 12. L(infinity)-estimates.- 13. Linear elliptic systems.- 14. The stationary Navier-Stokes system.- 15. Some more spaces.- 16. Regularity theory.- 17. The p-Laplace equation.- 18. The strong maximum principle.- 19. Problems in the whole space.- A. Fixed point theorems.- Bibliography.- Index.

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Details

  • NCID
    BA89347329
  • ISBN
    • 9783764399818
  • Country Code
    sz
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Basel
  • Pages/Volumes
    viii, 288 p
  • Size
    24 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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