| Document Type
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BL
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| Record Number
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1030401
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| Doc. No
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b784771
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| Main Entry
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Fraenkel, L. E.
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| Title & Author
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An introduction to maximum principles and symmetry in elliptic problems /\ L.E. Fraenkel.
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| Publication Statement
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Cambridge, UK ;New York, NY, USA :: Cambridge University Press,, 2000.
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| Series Statement
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Cambridge tracts in mathematics ;; 128
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| Page. NO
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x, 340 pages :: illustrations ;; 24 cm.
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| ISBN
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0521461952
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: 9780521461955
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| Bibliographies/Indexes
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Includes bibliographical references (pages 332-336) and index.
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| Contents
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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.
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| Abstract
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"This is 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."--Jacket.
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| Subject
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Differential equations, Elliptic, Problems, exercises, etc.
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| Subject
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Differential equations, Elliptic.
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| Subject
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Maximum principles (Mathematics)
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| Subject
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Symmetry.
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| Subject
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Differential equations, Elliptic, Problems, exercises, etc.
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| Subject
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Differential equations, Elliptic.
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| Subject
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Elliptische Differentialgleichung
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| Subject
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Équations différentielles elliptiques.
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| Subject
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Maximum principles (Mathematics)
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| Subject
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Maximum principles (Mathematics)
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| Subject
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Principes du maximum (mathématiques)
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| Subject
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Symmetry.
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| Subject
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Elliptische differentiaalvergelijkingen.
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| Dewey Classification
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515.353
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| LC Classification
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QA377.F73 2000
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| NLM classification
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31.45bcl
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