An Introduction to Maximum Principles and Symmetry in Elliptic Problems.

Fraenkel, L E:

ISBN 10: 0521461952 / ISBN 13: 9780521461955

Published by Cambridge University Press, 2000

About this Item

Series: Cambridge Tracts in Mathematics. x 340p sturdy hardback, navy cloth with light blue jacket, very good condition, minimal wear, jacket a bit scruffy at the edges, spine sunned, binding firm, pages clean and bright, no marks or highlighting, a very good copy of an uncommon title Language: English Weight (g): 615.

Seller Inventory # 233742

Bibliographic Details

• Title: An Introduction to Maximum Principles and Symmetry in Elliptic Problems.
• Publisher: Cambridge University Press
• Publication Date: 2000
• Language: English
• ISBN 10: 0521461952
• ISBN 13: 9780521461955
• Binding: Hardback
• Edition: 1st Edition
• Condition: Very Good
• Dust Jacket Condition: Dust Jacket Included
• Weight: 615 grams
• Seller catalogs:
  • Mathematics

About this title

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.

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.