Introduction to the Theory of Linear Partial Differential Equations
Published on 14. May 2014
574 pages
978-0-08-087535-4 (ISBN)
Description
Introduction to the Theory of Linear Partial Differential Equations
More details
Series
Language
English
Place of publication
Burlington
Netherlands
Product notice
Windows
ISBN-13
978-0-08-087535-4 (9780080875354)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
J. Chazarain | A. Piriou
Introduction to the Theory of Linear Partial Differential Equations: Volume 14
Book
04/2000
North-Holland
€107.70
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Content
- Front Cover
- Introduction to the Theory of Linear Partial Differential Equations
- Copyright Page
- TABLE OF CONTENTS
- FOREWORD
- Chapter 1. Distributions and operators
- 1. Spaces of distributions
- 2. Convolution and Fourier transformation of distributions
- 3. Singular spectrum of a distribution
- 4. Operators and kernels
- 5. Operators and support properties
- 6. Differential operators with constant coefficients
- 7. Operators and distributions on a manifold
- 8. Operators and kernel distributions on a manifold
- 9. Regular open subsets of Rn and manifolds with boundary
- 10. Additional notes and exercises
- Chapter 2. Sobolev spaces and applications
- 1. Dirichlet's principle
- 2. The spaces Hs(Rn) and Hsloc(X)
- 3. The spaces Hs (X) and Hsloc(X)
- 4. Trace theorems, spaces Hso(X)
- 5. Application to the Dirichlet problem
- 6. Sobolev spaces and regularisation
- 7. Additional notes and exercises
- Chapter 3. Symbols, oscillatory integrals and stationary-phase theorems
- 1. Introduction
- 2. Symbols
- 3. Elliptic symbols
- 4. Asymptotic expansions of symbols
- 5. Topology on the symbol spaces
- 6. Various generalisations
- 7. Oscillatory integrals
- 8. Integral operators associated with a phase and an amplitude
- 9. Stationary-phase theorem
- 10. Additional notes and exercises
- Chapter 4. Pseudo differential operators
- 1. Definition
- 2. A characterisation of p.d.o.'s
- 3. Symbol of a p.d.o.
- 4. Algebra and symbolic calculus of p.d.o.'s
- 5. P.d.o.'s on manifolds
- 6. Symbolic calculus of p.d.o.'s on a manifold
- 7. Elliptic p.d.o.'s
- 8. P.d.o.'s and Sobolev spaces
- 9. Elliptic complexes and Hodge's theorem
- 10. Friedrich's lemma and generalisations
- 11. Additional notes and exercises
- Chapter 5. Elliptic boundary-value problems
- 1. Introduction
- 2. Regularity of the potential at the boundary
- 3. The Calderón projector
- 4. Application to elliptic boundary-value problems
- 5. Examples
- 6. Additional notes and exercises
- Chapter 6. Evolution equations
- 1. The Cauchy-Kovaleski and Holmgren theorems
- 2. Necessary condition for the Cauchy problem to be well posed
- 3. Hyperbolic operators with constant coefficients
- 4. Hyperbolic Cauchy problems with variable coefficients
- 5. Parabolic Cauchy problems
- 6. Semigroups of operators and applications
- 7. Additional notes and exercises
- Chapter 7. Mixed hyperbolic problems
- 1. Introduction
- 2. Operators and spaces used
- 3. The uniform Lopatinski condition
- 4. Energy inequalities
- 5. Construction of the symmetriser
- 6. Solution of the problem without initial conditions
- 7. Solution of the mixed problem
- 8. Finite propagation speed
- 9. Additional notes and exercises
- Chapter 8. Microlocalisation
- 1. General properties of the singular spectrum (WF)
- 2. The fundamental theorems
- 3. The case of manifolds
- 4. The case of pseudo-differential operators
- 5. Additional notes and exercises
- Bibliography
- Index
