The analysis of solutions of elliptic equations
Author(s)
Bibliographic Information
The analysis of solutions of elliptic equations
（Mathematics and its applications, v. 406）
Kluwer, c1997
- Other Title
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Ряд Лорана для решений эллиптических систем
Ri︠a︡d Lorana dli︠a︡ resheniĭ ėllipticheskikh sistem
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
515.353/T1742070403598
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Note
Updated and rev. translation of: Ряд Лорана для решений эллиптических систем. Новосибирск : Наука, c1991
Includes bibliographical references (p. 451-471) and indexes
Description and Table of Contents
Description
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.
Table of Contents
Prefaces. List of Main Notations. 1. Removable Singularities. 2. Laurent Series. 3. Representation of Solutions with Non-Discrete Singularities. 4. Uniform Approximation. 5. Mean Approximation. 6. BMO Approximation. 7. Conditional Stability. 8. The Cauchy Problem. 9. Quasiconformality. Bibliography. Name Index. Subject Index. Index of Notation.
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