Partial Differential Equations: Elliptic and Parabolic Operators

Yu.V. Egorov, M. A. Shubin, R. Cooke et Marek Capinski

ISBN 10: 3540546782 / ISBN 13: 9783540546788

Published by Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1994

About this Item

Ancien livre de bibliothèque. Edition 1994. Tome 63. Ammareal reverse jusqu'à 15% du prix net de cet article à des organisations caritatives. ENGLISH DESCRIPTION Book Condition: Used, Very good. Former library book. Edition 1994. Volume 63. Ammareal gives back up to 15% of this item's net price to charity organizations. Seller Inventory # E-571-450

Bibliographic Details

Title: Partial Differential Equations: Elliptic and...

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K

Publication Date: 1994

Binding: Hardcover

Condition: Très bon

About this title

Synopsis:

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.