Introduction to the Theory of Linear Partial Differential Equations (Studies in mathematics and its applications) - ISBN:0444864520

Introduction to the Theory of Linear Partial Differential Equations (Studies in mathematics and its applications)

Date: 10 April 2011, 01:25

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FOREWORD
Since the fifties, the theory of partial differential equations has undergone considerable development , yet it is certainLy one of those fields where we find both the largest number of research articles and the smallest number of works of synthesis. The specialist can come to terms with such a situation, but the student who desires an introduction to this theory finds it rather a handicap. treatise but an introduction, we aim to present a reasonably large range of recent methods: pseudo-differential operators, oscillatory integrals, stationary phase expansion, microlocalisation .... We show how these methods permit the solution of numerous classical problems in an elegant and general manner: elliptic equations, boundary problems, evolution equations, mixed hyperbolic problems,... , We have allotted considerable room to the equations of Physics because, historically, this has been the origin of important problems in partial differential equations and remains to the present day the principal source of interesting questions.
Thus, in the present book, which is not a As regards the form of the book, we have endeavoured to give very detailed proofs in such a way as to render the work accessible to a reader at post-graduate level. have sometimes preferred to restrict to some degree the generality
With this in mind, we have sometimes preferred to restrict to some degree the generality of certain results in order to avoid obscuring the ideas- underlying the techniques being used. Each chapter begins, in general, with a brief description of the subject matter and the methods which will be developed therein, and ends with supplements in the form of exercises together with hints for solution (an asterisk indicates those which will be utilised in the text which follows). For the convenience of the reader, the main extensions are listed within the table of contents.
The bibliography given is deliberately restricted: anyone writing on such a subject refers to such a large number of sources that an exhaustive list of these would be unwieldy. For the convenience of the reader, the main extensions
It seems to us to be possible to use this book at two levels; on the one hand the first four Chapters (Distributions and Operators; Sobolev Spaces; Symbols and Oscillatory Integrals; Pseudo-differential Operators) can serve as the basis for an introductory post-graduate course. On the other hand, the last four Chapters (Elliptic boundary problems; Evolution equations; Mixed hyperbolic problems; Microlocalisation) are aimed more particularly at Ph.D. students and at research workers who will find contained therein numerous results formerly dispersed amongst specialised journals.

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