Abstract
We are going to define Sobolev spaces of integer order on a Riemannian manifold. First we shall be concerned with density problems. Then we shall prove the Sobolev imbedding theorem and the Kondrakov theorem. After that we shall introduce the notion of best constant in the Sobolev imbedding theorem. Finally, we shall study the exceptional case of this theorem (i.e., H n1 on n-dimensional manifolds).
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© 1998 Springer-Verlag Berlin Heidelberg
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Aubin, T. (1998). Sobolev Spaces. In: Some Nonlinear Problems in Riemannian Geometry. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13006-3_2
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DOI: https://doi.org/10.1007/978-3-662-13006-3_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08236-8
Online ISBN: 978-3-662-13006-3
eBook Packages: Springer Book Archive