Chapter 4

Sobolev Spaces

Erhan Pişkin* and Baver Okutmuştur*

Abstract

Sobolev spaces were defined by the Russian mathematician Sergei Lvovich Sobolev (1908-1989) in the 1930s. Denoted by Wm;p (Ω) ; Sobolev spaces are the space of functions whose all m-th order generalized derivatives are in Lp (Ω) space and partial derivatives of these spaces satisfy certain integrability conditions. Notice that generalized derivative refers to the weak derivative which is defined in the previous chapter. In this part we present fundamental properties of Sobolev spaces with several examples. For further reading on Sobolev spaces we cite [29–32].

Total Pages: 97-118 (22)

Purchase Chapter  Book Details