Overview

This volume is the first to be devoted to the study of various properties of wide classes of degenerate elliptic operators of arbitrary order and pseudo-differential operators with multiple characteristics. Conditions for operators to be Fredholm in appropriate weighted Sobolev spaces are given, a priori estimates of solutions are derived, inequalities of the Garding type are proved, and the principal term of the spectral asymptotics for self-adjoint operators is computed. A generalization of the classical Weyl formula is proposed. Some results are new, even for operators of the second order. In addition, an analogue of the Boutet de Monvel calculus is developed and the index is computed. For postgraduate and research mathematicians, physicists and engineers whose work involves the solution of partial differential equations.

Full Product Details

Author:   Serge Levendorskii
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of hardcover 1st ed. 1993
Volume:   258
Dimensions:   Width: 21.00cm , Height: 2.30cm , Length: 29.70cm
Weight:   1.177kg
ISBN:  

9789048142828

ISBN 10:   9048142822
Pages:   436
Publication Date:   15 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

0 Introduction.- 1 General Calculus of Pseudodifferential Operators.- 2 Model Classes of Degenerate Elliptic Differential Operators.- 3 General Classes of Degenerate Elliptic Differential Operators.- 4 Degenerate Elliptic Operators in Non — Power — Like Degeneration Case.- 5 Lp — Theory for Degenerate Elliptic Operators.- 6 Coersiveness of Degenerate Quadratic Forms.- 7 Some Classes of Hypoelliptic Pseudodifferential Operators on Closed Manifold.- 8 Algebra of Boundary Value Problems for Class of Pseudodifferential Operators which Change Order on the Boundary.- 9 General Schemes of Investigation of Spectral Asymptotics for Degenerate Elliptic Equations.- 10 Spectral Asymptotics of Degenerate Elliptic Operators.- 11 Spectral Asymptotics of Hypoelliptic Operators with Multiple Characteristics.- A Brief Review of the Bibligraphy.- Index of Notation.

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