The Analysis of Solutions of Elliptic Equations - Couverture rigide

Tarkhanov, Nikolai

Couverture rigide

ISBN 10 : 0792345312 ISBN 13 : 9780792345312

Editeur : Kluwer Academic Publishers, 1997

Synopsis

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.

A propos du livre

Présentation de l'éditeur

This volume focuses on the analysis of solutions to general elliptic equations. A wide range of topics is touched upon, such as removable singularities, Laurent expansions, approximation by solutions, Carleman formulas, quasiconformality. While the basic setting is the Dirichlet problem for the Laplacian, there is some discussion of the Cauchy problem. Care is taken to distinguish between results which hold in a very general setting (arbitrary elliptic equation with the unique continuation property) and those which hold under more restrictive assumptions on the differential operators (homogeneous, of first order). Some parallels to the theory of functions of several complex variables are also sketched. Audience: This book will be of use to postgraduate students and researchers whose work involves partial differential equations, approximations and expansion, several complex variables and analytic spaces, potential theory and functional analysis. It can be recommended as a text for seminars and courses, as well as for independent study.

Détails de l'édition

• Éditeur: Kluwer Academic Publishers
• Date d'édition: 1997
• Langue: anglais
• ISBN 10: 0792345312
• ISBN 13: 9780792345312
• Reliure: Relié
• Nombre de pages: 504
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne