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有读书笔记Elliptic Partial Differential Equations (Courant Lecture Notes)

yhhuang 添加于 2010-1-15 06:37 | 2599 次阅读 | 1 个评论
  •  作 者

    Qing Han, Fanghua Lin
  •  摘 要

    This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame (IN). Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear, however, the presented methods also apply to nonlinear problems. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
  •  详细资料

    • 文献种类:书籍
    • 期卷页: 123
    • 出版社: American Mathematical Society
    • 日期: 2000-07-01
    • ISBN: 0821826913
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    Elliptic Partial Differential Equations

    In this short yet concise lecture notes, almost everything about Elliptic Partial Differential Equations is touched.

     

    Chapter 1 is about harmonic functions. The special property about harmonic function is the mean value formula and the simple for of the fundamental solution, from which we can get maximum principal and uniqueness. However, these properties cannot be extended to more general elliptic functions, even for those with constant coefficients. The maximum principle in general form and the energy method in the last two sections are more useful.

     

    Chapter 2 is about maximum principle. The classical maximum principles are introduced from which we can derive apriori bounds on the solutions and the gradients. Alexandrov type maximum principle are very powerful for quasilinear equations like those for curvature equations, Monge-Ampere equations.

     

     

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!reply! yha82 2010-12-26 03:21
short book about Elliptic PDEs

facelist doodle 涂鸦板

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