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portada An Introduction to Maximum Principles and Symmetry in Elliptic Problems Hardback (Cambridge Tracts in Mathematics)
Type
Physical Book
Publisher
Author
Year
2000
Language
English
Pages
352
Format
Hardcover
ISBN
0521461952
ISBN13
9780521461955
Edition No.
1
Categories

An Introduction to Maximum Principles and Symmetry in Elliptic Problems Hardback (Cambridge Tracts in Mathematics)

Fraenkel (Author) · Cambridge University Press · Hardcover

An Introduction to Maximum Principles and Symmetry in Elliptic Problems Hardback (Cambridge Tracts in Mathematics) - Fraenkel

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Synopsis "An Introduction to Maximum Principles and Symmetry in Elliptic Problems Hardback (Cambridge Tracts in Mathematics) "

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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