An Introduction to Maximum Principles and Symmetry in Elliptic Problems

An Introduction to Maximum Principles and Symmetry in Elliptic Problems

An Introduction to Maximum Principles and Symmetry in Ellic Problems (Cambridge Tracts in Mathematics) by L. E. Fraenkel
English | Apr 13, 2000 | ISBN: 0521461952 | 351 Pages | PDF | 2 MB

This book presents the basic theory of the symmetry of solutions to second-order ellic 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 ellic equations.
Gidas, Ni and Nirenberg, building on the work of Alexandrov and Serrin, have shown that the shape of the set on which such ellic 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.


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