Name: Symmetry Problems (en Inglés)
Price: 199488.00 COP
Availability: InStock
Author: Alexander G. Ramm
ISBN: 9783031035432

Formato

Libro Físico

Editorial

Springer Nature B.V.

Autor

Alexander G. Ramm

Año

2019

Idioma

Inglés

N° páginas

Encuadernación

Tapa Blanda

Dimensiones

23.5 x 19.1 cm

ISBN13

9783031035432

Symmetry Problems (en Inglés)

Alexander G. Ramm (Autor) · Springer Nature B.V. · Tapa Blanda

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Reseña del libro "Symmetry Problems (en Inglés)"

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.