The Technion school lecture notes: the moving plane method, or doing PDEs in a café

نویسنده

  • Lenya Ryzhik
چکیده

We will have two main characters in these notes: the maximum principle and the sliding method. The latter has a twin, the moving plane method – they are often so indistinguishable that we will count them as one character. They will be introduced separately, and then blended together to prove the symmetry properties of the solutions of elliptic equations. In this introductory section, we recall the what the maximum principle is. This material is very standard and can be found in almost any undergraduate or graduate PDE text, such as the books by Evans [7], Han and Lin [10], and Pinchover and Rubinstein [11]. We will consider equations of the form

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تاریخ انتشار 2014