An Introduction to Maximum Principles and Symmetry in Elliptic Problems: 128 (Cambridge Tracts in Mathematics, Series Number 128) - Softcover

Fraenkel, L. E.

Softcover

ISBN 10: 0521172780 ISBN 13: 9780521172783

Publisher: Cambridge University Press, 2011

Synopsis

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.

About this title

Review

Review of the hardback: 'The originality of this book mainly consists in new proofs and new extensions of quite well known results concerning maximum principles and symmetry properties related to semilinear elliptic equations.' Mathematical Reviews

Book Description

The author of this 2000 volume proceeds from elementary facts about the linear case to recent results about positive solutions of non-linear elliptic equations, with minimal prerequisites in a style suited to graduate students. There is a plentiful supply of exercises, with detailed hints, some of which contain new results.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2011
• Language: English
• ISBN 10: 0521172780
• ISBN 13: 9780521172783
• Binding: Paperback
• Number of pages: 352