Format:
1 Online-Ressource (x, 340 pages)
,
digital, PDF file(s).
ISBN:
9780511569203
Series Statement:
Cambridge tracts in mathematics 128
Content:
Originally published in 2000, this was the first book to present 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 non-linear elliptic equations. Gidas, Ni and Nirenberg, building on work of Alexandrov and of 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. Results are presented with minimal prerequisites in a style suited to graduate students. Two long and leisurely appendices give basic facts about the Laplace and Poisson equations. There is a plentiful supply of exercises, with detailed hints.
Content:
Some Notation, Terminology and Basic Calculus -- 1. Introduction -- 2. Some Maximum Principles for Elliptic Equations -- 3. Symmetry for a Non-linear Poisson Equation in a Symmetric Set [Omega] -- 4. Symmetry for the Non-linear Poisson Equation in R[superscript N] -- 5. Monotonicity of Positive Solutions in a Bounded Set [Omega] -- App. A. On the Newtonian Potential -- App. B. Rudimentary Facts about Harmonic Functions and the Poisson Equation -- App. C. Construction of the Primary Function of Siegel Type -- App. D. On the Divergence Theorem and Related Matters -- App. E. The Edge-Point Lemma
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Additional Edition:
ISBN 9780521172783
Additional Edition:
ISBN 9780521461955
Additional Edition:
ISBN 9780521461955
Additional Edition:
ISBN 9780521172783
Additional Edition:
Erscheint auch als Fraenkel, L. E. An introduction to maximum principles and symmetry in elliptic problems Cambridge [u.a.] : Cambridge University Press, 2000 ISBN 0521461952
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9780521461955
Language:
English
Subjects:
Mathematics
Keywords:
Elliptische Differentialgleichung
;
Symmetrie
;
Maximumprinzip
DOI:
10.1017/CBO9780511569203
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