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The Analysis of Solutions of Elliptic Equations : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - Nikolai Tarkhanov

The Analysis of Solutions of Elliptic Equations

MATHEMATICS AND ITS APPLICATIONS (KLUWER )

Hardcover Published: 30th April 1997
ISBN: 9780792345312
Number Of Pages: 484

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This book is intended as a continuation of my book "Parametrix Method in the Theory of Differential Complexes" (see [291]). There, we considered complexes of differential operators between sections of vector bundles and we strived more than for details. Although there are many applications to for maximal generality overdetermined systems, such an approach left me with a certain feeling of dissat- faction, especially since a large number of interesting consequences can be obtained without a great effort. The present book is conceived as an attempt to shed some light on these new applications. We consider, as a rule, differential operators having a simple structure on open subsets of Rn. Currently, this area is not being investigated very actively, possibly because it is already very highly developed actively (cf. for example the book of Palamodov [213]). However, even in this (well studied) situation the general ideas from [291] allow us to obtain new results in the qualitative theory of differential equations and frequently in definitive form. The greater part of the material presented is related to applications of the L- rent series for a solution of a system of differential equations, which is a convenient way of writing the Green formula. The culminating application is an analog of the theorem of Vitushkin [303] for uniform and mean approximation by solutions of an elliptic system. Somewhat afield are several questions on ill-posedness, but the parametrix method enables us to obtain here a series of hitherto unknown facts.

`Summarising this is a well-written book. It provides the complete survey of the history and the recent state of the subject topic. The book will be of use to postgraduate students and researchers in PDE's, in theory of approximations and expansions, in potential theory or in functional analysis. It is warmly recommended as a text for seminars and courses, as well as for independent study for everyone with a basic knowledge on distributions and pseudodifferential operators.' Acta Scientiarum Mathematicarum

Preface to the English Translation
Preface to the Russian Edition
List of Main Notationsp. 1
Removable Singularitiesp. 5
Laurent Seriesp. 67
Representation of Solutions with Non-Discrete Singularitiesp. 115
Uniform Approximationp. 191
Mean Approximationp. 271
BMO Approximationp. 319
Conditional Stabilityp. 345
The Cauchy Problemp. 373
Quasiconformalityp. 411
Bibliographyp. 451
Name Indexp. 472
Subject Indexp. 475
Index of Notationp. 478
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792345312
ISBN-10: 0792345312
Series: MATHEMATICS AND ITS APPLICATIONS (KLUWER )
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 484
Published: 30th April 1997
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 25.4 x 17.78  x 3.81
Weight (kg): 1.04