1.—Perturbation Theory for Sobolev Spaces

Proceedings of the Royal Society of Edinburgh Section A: Mathematics - Tập 73 - Trang 5-49 - 1975
Friedrich Stummel1
1Department of Mathematics, Johann Wolfgang Goethe Universität, Frankfurt am Main

Tóm tắt

SynopsisThis 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.

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Tài liệu tham khảo

Adams, 1970, Capacity and compact imbeddings, J.Math. Mech., 19, 923

Nečas, 1967, Les méthodes directes en theorie des équations elliptiques

Agmon, 1965, Lectures on elliptic boundary value problems

10.1007/BF01349967

10.1090/S0002-9904-1967-11818-4

10.1007/BF01427953

Friedman, 1969, Partial differential equations

14 Stummel F. , Singular perturbations of elliptic sesquilinear forms. Proc. Confer. Differential Equations, Dundee, 1972: Lecture Notes in Mathematics, 280, 155–180. Berlin: Springer, 1972.

Stummel, 1973, Approximation methods in analysis, Lecture Notes Series, Aarhus Univ., Mat.Inst., 35

Hausdorff, 1965, Grundzüge der Mengenlehre.

10.1073/pnas.51.6.1055

Dunford, 1958, Linear operators.

10.4153/CJM-1971-055-3

Stummel, 1969, Lecture Notes in Mathematics, 102

Morrey, 1966, Multiple integrals in the calculus of variations, 10.1007/978-3-540-69952-1

Stummel, 1972, Proc. Confer. Numer. Anal.

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Thông tin xuất bản

Proceedings of the Royal Society of Edinburgh Section A: Mathematics

Tập 73

5-49

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