Lecture Notes on “A Basic Course in Elliptic Differential Equations” Van Abel 02/26/2012

摘要 . This notes is based on the lectures which was given by Prof. Jiayu Li in Science and Technology University of China juring the second semester of 2011.

The original content were the notes take by a someone (I don’t know her name, and hopefully add it at sometime later), it is detailed and elegant. I want to share it with others, and make it more perfect by adding some problems and re-typeset it by latex.

I have added subsections to the contents to make it more readable, and some problems which occurs to me when I go through it. The excise is almost leaved by the lecturer and the idea or some important words or comments on the content given by the lecturer will added as remark or quote.

I would like to thank G. H. Qiu for his help and the original notes taker for hers detailed work.

I shall be responsible for any error in this notes. Any improvement of this notes are welcome, this is my first intention to make the notes available in E-book. Therefore, if you find any errors or have any suggestions, please contact me by

E-Mail: [email protected] This notes also available on the WaMatH site: wamath.sinaapp.com.

Contents

Contents
1.  Harmonic Functions
1.1.  Harmonic Functions and Fundamental Solution of Laplace Equation
1.2.  Green’s Formula and Green’s Identity
1.3.  Green’s Function and Its Properties

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