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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
An Introduction to Maximum Principles and Symmetry in Elliptic Problems

An Introduction to Maximum Principles and Symmetry in Elliptic Problems

Fraenkel, L. E.
Bollobas, Bela
L. E., Fraenkel

Hardcover

Series: Cambridge Tracts in Mathematics, Book 128

General Mathematics

ISBN10: 0521461952
ISBN13: 9780521461955
Publisher: Cambridge University Press
Published: Feb 25 2000
Pages: 352
Weight: 1.33
Height: 0.93 Width: 6.48 Depth: 9.18
Language: English
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.

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