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An Introduction to Maximum Principles and Symmetry in Elliptic Problems by L.E. Fraenkel
An Introduction to Maximum Principles and Symmetry in Elliptic Problems by L.E. Fraenkel
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An Introduction to Maximum Principles and Symmetry in Elliptic Problems

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Description

Originally 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.
Release date Australia
April 14th, 2011
Author
Audience
  • Professional & Vocational
Pages
352
Dimensions
152x229x20
ISBN-13
9780521172783
Product ID
7934565

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An Introduction to Maximum Principles and Symmetry in Elliptic Problems on Hardback by L.E. Fraenkel
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