Partial Differential Equations VI : Elliptic and Parabolic Operators

Yu. V. Egorov

ISBN 10: 3642081177 / ISBN 13: 9783642081170

Verlag: Springer Berlin Heidelberg, 2010

Beschreibung

Druck auf Anfrage Neuware - Printed after ordering - 0. 1. The Scope of the Paper. This article is mainly devoted to the oper ators indicated in the title. More specifically, we consider elliptic differential and pseudodifferential operators with infinitely smooth symbols on infinitely smooth closed manifolds, i. e. compact manifolds without boundary. We also touch upon some variants of the theory of elliptic operators in !Rn. A separate article (Agranovich 1993) will be devoted to elliptic boundary problems for elliptic partial differential equations and systems. We now list the main topics discussed in the article. First of all, we ex pound theorems on Fredholm property of elliptic operators, on smoothness of solutions of elliptic equations, and, in the case of ellipticity with a parame ter, on their unique solvability. A parametrix for an elliptic operator A (and A-). . J) is constructed by means of the calculus of pseudodifferential also for operators in !Rn, which is first outlined in a simple case with uniform in x estimates of the symbols. As functional spaces we mainly use Sobolev £ - 2 spaces. We consider functions of elliptic operators and in more detail some simple functions and the properties of their kernels. This forms a foundation to discuss spectral properties of elliptic operators which we try to do in maxi mal generality, i. e. , in general, without assuming selfadjointness. This requires presenting some notions and theorems of the theory of nonselfadjoint linear operators in abstract Hilbert space. Bestandsnummer des Verkäufers 9783642081170

Bibliografische Details

Titel: Partial Differential Equations VI : Elliptic...

Verlag: Springer Berlin Heidelberg

Erscheinungsdatum: 2010

Einband: Taschenbuch

Zustand: Neu

Über diesen Titel

Inhaltsangabe:

This volume of the EMS contains three contributions covering topics in the field of partial differential equations. All the authors are well-known researchers and they present their material as accessible surveys, enabling readers to find comprehensive coverage of results which are scattered throughout the literature. For this reason the book is a unique source of information. It forms part of a multi-volume subseries of the EMS devoted to partial differential equations and it will be very useful to graduate students and researchers in mathematics and theoretical physics as well as engineers who are interested in this subject.

Reseña del editor:

Authored by well-known researchers, this book presents its material as accessible surveys, giving readers access to comprehensive coverage of results scattered throughout the literature. A unique source of information for graduate students and researchers in mathematics and theoretical physics, and engineers interested in the subject.