Elliptic Equations: An Introductory Course

ISBN-13: 9783764399818 / Angielski / Twarda / 2009 / 290 str.

Michel Chipot

Opis

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.

Recenzje

From the reviews:

"The present book is devoted to recent advanced results and methods in the theory of linear and nonlinear elliptic equations and systems. ... It is written with great care and is accessible to a large audience including graduate and postgraduate students and researchers in the field of partial differential equations. ... In conclusion, the reviewer may recommend the book as a very good reference for those seeking, new, modern, and powerful techniques in the modern approach of nonlinear elliptic partial differential equations." (Vicentiu D. Radulescu, Zentralblatt MATH, Vol. 1171, 2009)

"The book introduces the reader to a broad spectrum of topics in the theory of elliptic partial differential equations in a simple and systematic way. It provides a comprehensive introductory course to the theory, each chapter being supplemented with interesting exercises for the reader. ... The way of presentation of the material ... keep the reader's attention on the beauty and variety of the issues. ... a very valuable position in the field of elliptic partial differential equations." (Irena Pawlow, Control and Cybernetics, Vol. 39 (3), 2010)

Spis treści

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.