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Table of contents (6 chapters)
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Front Matter
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Back Matter
About this book
This book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It also gives necessary and sufficient conditions for a domain to be a ball if an overdetermined boundary problem for the Helmholtz equation in this domain is solvable. This includes a proof of Schiffer's conjecture, the solution to the Pompeiu problem, and other symmetry problems for partial differential equations. It goes on to study some other symmetry problems related to the potential theory. Among these is the problem of "invisible obstacles." In Chapter 5, it provides a solution to the Navier‒Stokes problem in ℝ³. The author proves that this problem has a unique global solution if the data are smooth and decaying sufficiently fast. A new a priori estimate of the solution to the Navier‒Stokes problem is also included. Finally, it delivers a solution to inverse problem of the potential theory without the standard assumptions about star-shapeness of the homogeneous bodies.
About the author
Bibliographic Information
Book Title: Symmetry Problems
Book Subtitle: The Navier–Stokes Problem
Authors: Alexander G. Ramm
Series Title: Synthesis Lectures on Mathematics & Statistics
DOI: https://doi.org/10.1007/978-3-031-02415-3
Publisher: Springer Cham
eBook Packages: Synthesis Collection of Technology (R0), eBColl Synthesis Collection 8
Copyright Information: Springer Nature Switzerland AG 2019
Softcover ISBN: 978-3-031-01287-7Published: 04 March 2019
eBook ISBN: 978-3-031-02415-3Published: 01 June 2022
Series ISSN: 1938-1743
Series E-ISSN: 1938-1751
Edition Number: 1
Number of Pages: XIV, 71
Topics: Mathematics, general, Statistics, general, Engineering Mathematics