A Review of Elliptic Theories

Abstract

In Chaps. 2–4 we shall review material from first year PDE courses. These theories can be found in many books such as Chen–Wu [21], Chen [20], Gilbarg–Trudinger [67], Lieberman [94]. Compared to others, the books [21] and [20] are not intim- idating even for beginners and therefore are excellent textbooks for beginning graduate students. The book [21] received the textbook excellence award from the education department of China. Some of the more classical theories can also be found in Ladyzenskaja–Solonnikov–Ural’ceva [83], Ladyzenskaja–Ural’ceva [84] and Friedman [43], and the classical maximum principles in Protter–Weinberger [118]. In this chapter we list the elliptic theories that we will need later on.