Elliptic Theory on Singular Manifolds: 1st Edition (Hardback) book cover

Elliptic Theory on Singular Manifolds

1st Edition

By Vladimir E. Nazaikinskii, Anton Yu. Savin, Bert-Wolfgang Schulze, Boris Yu. Sternin

Chapman and Hall/CRC

376 pages

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Description

The analysis and topology of elliptic operators on manifolds with singularities are much more complicated than in the smooth case and require completely new mathematical notions and theories. While there has recently been much progress in the field, many of these results have remained scattered in journals and preprints.

Starting from an elementary level and finishing with the most recent results, this book gives a systematic exposition of both analytical and topological aspects of elliptic theory on manifolds with singularities. The presentation includes a review of the main techniques of the theory of elliptic equations, offers a comparative analysis of various approaches to differential equations on manifolds with singularities, and devotes considerable attention to applications of the theory. These include Sobolev problems, theorems of Atiyah-Bott-Lefschetz type, and proofs of index formulas for elliptic operators and problems on manifolds with singularities, including the authors' new solution to the index problem for manifolds with nonisolated singularities.

A glossary, numerous illustrations, and many examples help readers master the subject. Clear exposition, up-to-date coverage, and accessibility-even at the advanced undergraduate level-lay the groundwork for continuing studies and further advances in the field.

Table of Contents

Singular Manifolds and Differential Operators. Analytical Tools. Topological Problems. Applications and Related Topics. Appendices. Biographical Remarks. Bibliography. Index.

About the Authors

Nazaikinskii, Vladimir E.; Savin, Anton Yu.; Schulze, Bert-Wolfgang; Sternin, Boris Yu.

About the Series

Differential and Integral Equations and Their Applications

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT007000
MATHEMATICS / Differential Equations
MAT012000
MATHEMATICS / Geometry / General
SCI040000
SCIENCE / Mathematical Physics