An Introduction to Maximum Principles and Symmetry in Elliptic Problems
By (author) L. E. Fraenkel
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Introduction to Maximum Principles and Symmetry in Elliptic Problems by L. E. Fraenkel
Book DescriptionOriginally published in 2000, this was the first book to present the basic theory of the symmetry of solutions to second-order elliptic partial differential equations by means of the maximum principle. It proceeds from elementary facts about the linear case to recent results about positive solutions of non-linear elliptic equations. Gidas, Ni and Nirenberg, building on work of Alexandrov and of Serrin, have shown that the shape of the set on which such elliptic equations are solved has a strong effect on the form of positive solutions. In particular, if the equation and its boundary condition allow spherically symmetric solutions, then, remarkably, all positive solutions are spherically symmetric. Results are presented with minimal prerequisites in a style suited to graduate students. Two long and leisurely appendices give basic facts about the Laplace and Poisson equations. There is a plentiful supply of exercises, with detailed hints.
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Book DetailsISBN: 9780521461955
(228mm x 152mm x 24mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 25-Feb-2000
Country of Publication: United Kingdom
Books By Author L. E. Fraenkel
Introduction to Maximum Principles and Symmetry in Elliptic Problems, Paperback (December 2010)» View all books by L. E. Fraenkel
Advanced text, originally published in 2000, on differential equations, with plentiful supply of exercises all with detailed hints.
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