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An Introduction to Maximum Principles and Symmetry in Elliptic Problems (Cambridge Tracts in Mathematics, Series Number 128) - Softcover
Synopsis
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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Book Description
This is the first book to present the basic theory of the symmetry of solutions to second-order elliptic equations by means of the maximum principle. It proceeds from elementary facts about the linear case to recent results, 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 a plentiful supply of exercises, with detailed hints, some of which contain new results.
Review
"The originality of this book mainly consists in new proofs and new extensions of quite well known results concerning maximum principles and symmetry properties related to semilinear elliptic equations." Mathematical Reviews
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An Introduction to Maximum Principles and Symmetry in Elliptic Problems (Cambridge Tracts in Mathematics, Series Number 128)
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An Introduction to Maximum Principles and Symmetry in Elliptic Problems (Cambridge Tracts in Mathematics, Series Number 128)
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ISBN 13: 9780521172783
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An Introduction to Maximum Principles and Symmetry in Elliptic Problems: 128 (Cambridge Tracts in Mathematics, Series Number 128)
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An Introduction to Maximum Principles and Symmetry in Elliptic Problems: 128 (Cambridge Tracts in Mathematics, Series Number 128)
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Condition: New. Advanced text, originally published in 2000, on differential equations, with plentiful supply of exercises all with detailed hints. Series: Cambridge Tracts in Mathematics. Num Pages: 352 pages, black & white illustrations, figures. BIC Classification: PBKJ. Category: (P) Professional & Vocational. Dimension: 155 x 228 x 29. Weight in Grams: 540. . 2011. Illustrated. paperback. . . . . Books ship from the US and Ireland. Seller Inventory # V9780521172783
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An Introduction to Maximum Principles and Symmetry in Elliptic Problems
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An Introduction to Maximum Principles and Symmetry in Elliptic Problems
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