【论坛首发】An Introduction to Maximum Principles and Symmetry in Elliptic Probl

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An Introduction to Maximum Principles and Symmetry in Elliptic Problems (2000).pdf (2.55 MB, 需要: 3 个论坛币)

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An Introduction to Maximum Principles and Symmetry in Elliptic Problems (Cambridge Tracts in Mathematics)

2000年版， 作者： L. E. Fraenkel
共351页

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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关键词：introduction troduction Principles principle Symmetry positive building recent about

最大原则和对称的椭圆问题简介（大港剑桥数学）

这本书提出的解决方案二阶椭圆型偏微分方程的对称通过的最大原则，方式的基本理论。它继续从约线性案件基本事实有关的非线性椭圆方程正解的最新成果。 Gidas，Ni和尼伦伯格，建立在亚历山德罗夫和Serrin的工作，表明在此种椭圆方程解集的形状有正解的形式有很强的影响。特别是，如果该方程及其边界条件允许球对称解决方案，所有的正解是显着球对称的。这些最近的和重要的结果都带有最少的先决条件，在适合研究生风格。两条长长的附录给出一个悠闲的帐户有关的拉普拉斯和泊松方程的基本事实，并有丰富的练习，有详细的提示，其中一些包含了最新成果。

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上面的书名翻译乱七八糟：椭圆问题中的极大值原理与对称性！

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