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1.—Perturbation Theory for Sobolev Spaces

Published online by Cambridge University Press:  14 February 2012

Friedrich Stummel
Friedrich Stummel
Affiliation:
Department of Mathematics, Johann Wolfgang Goethe Universität, Frankfurt am Main
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Synopsis

This paper studies Sobolev spaces under perturbation of domains of definition. It establishes the basic concepts, methods and results for the convergence of sequences of sets in ℝn, the strong and weak convergence of sequences of Sobolev spaces, the discrete compactness of natural embeddings and the continuous convergence of continuous linear functionals, boundary integrals and trace operators for sequences of Sobolev spaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 73 , 1975 , pp. 5 - 49
Copyright
Copyright © Royal Society of Edinburgh 1975

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