1st Edition

Elliptic Theory on Singular Manifolds

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ISBN 9781584885207
Published August 12, 2005 by Chapman and Hall/CRC
376 Pages

USD $185.00

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Book 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.

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

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Author - Vladimir E Nazaikinskii

Vladimir E Nazaikinskii

D.Sc./Senior Researcher, Institute for Problems in Mechanics, RAS

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