Sobolev Spaces

In this chapter, we review definitions and properties of Sobolev spaces, which are indispensable for a theoretical analysis of partial differential equations and boundary integral equations, as well as being necessary for the analysis of some numerical methods for solving such equations. Most results are stated without proof; proofs of the results and detailed discussions of Sobolev spaces can be found in numerous monographs and textbooks, e.g. [1, 63, 74, 210].