In order to study the variational formulations of boundary integral equations and their numerical approximations, one needs proper function spaces. The Sobolev spaces provide a very natural setting for variational problems. This chapter contains a brief summary of the basic definitions and results of the L2–theory of Sobolev spaces which will suffice for our purposes. A more general discussion on these topics may be found in the standard books such as Adams [1], Grisvard [108], Lions and Magenes [190], Maz'ya [201] and also in McLean [203].
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Sobolev Spaces. In: Boundary Integral Equations. Applied Mathematical Sciences, vol 164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68545-6_4
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DOI: https://doi.org/10.1007/978-3-540-68545-6_4
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