Abstract
The first section of this chapter is dedicated to the basic definitions and properties of domains in ℝd. We particularly focus our attention on the case of Lipschitz domains for which we can easily define an integration theory on ∂Ω, the outward unit normal on ∂Ω, and finally prove the Stokes formula which is the keystone of the study of partial differential equations on domains.
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© 2013 Springer Science+Business Media New York
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Boyer, F., Fabrie, P. (2013). Sobolev spaces. In: Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models. Applied Mathematical Sciences, vol 183. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5975-0_3
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DOI: https://doi.org/10.1007/978-1-4614-5975-0_3
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-5974-3
Online ISBN: 978-1-4614-5975-0
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