Elliptic Theory on Singular Manifolds

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

Sommario

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

Info autore

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

Riassunto

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.

Dettagli sul prodotto

• Autori: Vladimir E Nazaikinskii, Vladimir E. Nazaikinskii, Vladimir E. (Institute for Problems Nazaikinskii, Vladimir E. Savin Nazaikinskii, Nazaikinskii Vladimir E., Anton Yu Savin, Anton Yu. Savin, Savin Anton Yu., Bert-Wolfgang Schulze, Schulze Bert-Wolfgang, Boris Yu Sternin, Boris Yu. Sternin
• Editore: Taylor & Francis Ltd.
• Lingue: Inglese
• Formato: Tascabile
• Pubblicazione: 31.08.2019
• EAN: 9780367392291
• ISBN: 978-0-367-39229-1
• Pagine: 376
• Serie: Differential and Integral Equations and Their Applications
• Categorie: Scienze naturali, medicina, informatica, tecnica > Matematica > Tematiche generali, enciclopedie; MATHEMATICS / General, MATHEMATICS / Differential Equations / General, SCIENCE / Physics / Mathematical & Computational, MATHEMATICS / Geometry / General, geometry, Mathematical physics, Differential calculus & equations, Applied mathematics, Differential calculus and equations, Mathematical / Computational / Theoretical physics