Elliptic Theory on Singular Manifolds

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

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English

Chapman & Hall/CRC
25 September 2019

Differential calculus & equations; Geometry; Mathematical physics

Series: Differential and Integral Equations and Their Applications

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.

By: Vladimir E. Nazaikinskii, Anton Yu. Savin, Bert-Wolfgang Schulze, Boris Yu. Sternin
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 254mm, Width: 178mm,
Weight: 453g
ISBN: 9780367392291
ISBN 10: 0367392291
Series: Differential and Integral Equations and Their Applications
Pages: 376
Publication Date: 25 September 2019
Audience: College/higher education , General/trade , Primary , ELT Advanced
Format: Paperback
Publisher's Status: Active

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