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＜電子ブック＞
The Analysis of Solutions of Elliptic Equations / by Nikolai Tarkhanov
(Mathematics and Its Applications ; 406)

版	1st ed. 1997.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	1997
本文言語	英語
大きさ	XX, 484 p : online resource
著者標目	*Tarkhanov, Nikolai author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Approximation theory LCSH:Functions of complex variables LCSH:Potential theory (Mathematics) LCSH:Functional analysis FREE:Differential Equations FREE:Approximations and Expansions FREE:Several Complex Variables and Analytic Spaces FREE:Potential Theory FREE:Functional Analysis
一般注記	List of Main Notations -- 1 Removable Singularities -- 2 Laurent Series -- 3 Representation of Solutions with Non-Discrete Singularities -- 4 Uniform Approximation -- 6 BMO Approximation -- 7 Conditional Stability -- 8 The Cauchy Problem -- 9 Quasiconformality -- Name Index -- Index of Notation 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 HTTP:URL=https://doi.org/10.1007/978-94-015-8804-1

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