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An introduction to maximum principle...

Fraenkel, L. E.

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An introduction to maximum principles and symmetry in elliptic problems

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	An introduction to maximum principles and symmetry in elliptic problems/ L.E. Fraenkel.
其他題名:	An Introduction to Maximum Principles & Symmetry in Elliptic Problems
作者:	Fraenkel, L. E.
出版者:	Cambridge :Cambridge University Press, : 2000.,
面頁冊數:	x, 340 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
內容註:	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.
標題:	Differential equations, Elliptic. -
電子資源:	https://doi.org/10.1017/CBO9780511569203
ISBN:	9780511569203

An introduction to maximum principles and symmetry in elliptic problems
Fraenkel, L. E.

An introduction to maximum principles and symmetry in elliptic problems[electronic resource] /An Introduction to Maximum Principles & Symmetry in Elliptic ProblemsL.E. Fraenkel. - Cambridge :Cambridge University Press,2000. - x, 340 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;128. - Cambridge tracts in mathematics ;128..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

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.

ISBN: 9780511569203Subjects--Topical Terms:

541859
Differential equations, Elliptic.

LC Class. No.: QA377 / .F73 2000

Dewey Class. No.: 515.353

An introduction to maximum principles and symmetry in elliptic problems
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505 0 $a 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.
520 $a 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.
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