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; detailed proofs of the results can be found in standard references on Sobolev spaces, e.g., .
KeywordsSobolev Space Spherical Harmonic Lipschitz Domain Lipschitz Boundary Part Formula
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