Book Details
Format
Paperback / Softback
Book Series
Lecture Notes in Mathematics
ISBN-10
3030674274
ISBN-13
9783030674274
Edition
1st ed. 2021
Publisher
Springer Nature Switzerland AG
Imprint
Springer Nature Switzerland AG
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Feb 13th, 2021
Print length
96 Pages
Product Classification:
Numerical analysisTopology
Ksh 8,100.00
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This book is devoted to computing the index of elliptic PDEs on non-compact Riemannian manifolds in the presence of local singularities and zeros, as well as polynomial growth at infinity.
This book is devoted to computing the index of elliptic PDEs on non-compact Riemannian manifolds in the presence of local singularities and zeros, as well as polynomial growth at infinity. The classical Riemann-Roch theorem and its generalizations to elliptic equations on bounded domains and compact manifolds, due to Maz''ya, Plameneskii, Nadirashvilli, Gromov and Shubin, account for the contribution to the index due to a divisor of zeros and singularities. On the other hand, the Liouville theorems of Avellaneda, Lin, Li, Moser, Struwe, Kuchment and Pinchover provide the index of periodic elliptic equations on abelian coverings of compact manifolds with polynomial growth at infinity, i.e. in the presence of a "divisor" at infinity.
The text is targeted towards researchers in PDEs, geometric analysis, and mathematical physics.
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