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

Fraenkel, L. E.

Hardcover

ISBN 10: 0521461952 ISBN 13: 9780521461955

Publisher: Cambridge University Press, 2000

Synopsis

This book presents 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 nonlinear elliptic equations. Gidas, Ni and Nirenberg, building on the work of Alexandrov and 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. These recent and important results are presented with minimal prerequisites, in a style suited to graduate students. Two long appendices give a leisurely account of basic facts about the Laplace and Poisson equations, and there is an abundance of exercises, with detailed hints, some of which contain new results.

About this title

Book Description

This is the first book to present the basic theory of the symmetry of solutions to second-order elliptic equations by means of the maximum principle. It proceeds from elementary facts about the linear case to recent results, presented with minimal prerequisites, in a style suited to graduate students. Two long appendices give a leisurely account of basic facts about the Laplace and Poisson equations, and there is a plentiful supply of exercises, with detailed hints, some of which contain new results.

Review

"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

Edition details

• Publisher: Cambridge University Press
• Publication date: 2000
• Language: English
• ISBN 10: 0521461952
• ISBN 13: 9780521461955
• Binding: Hardcover
• Edition number: 1
• Number of pages: 352