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Approximation numbers of Sobolev imbeddings over unbounded domains. (English) Zbl 0402.46023


MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35J65 Nonlinear boundary value problems for linear elliptic equations
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
47A10 Spectrum, resolvent
47F05 General theory of partial differential operators

Citations:

Zbl 0399.47018
Full Text: DOI

References:

[1] Adams, R. A., Capacity and compact imbeddings, J. Math. Mech., 19, 923-929 (1970) · Zbl 0193.41402
[2] Adams, R. A.; Fournier, J., Some imbedding theorems for Sobolev spaces, Canad. J. Math., 23, 517-530 (1971) · Zbl 0201.16301
[3] Agmon, S., Lectures on Elliptic Boundary Value Problems (1965), Van Nostrand: Van Nostrand New York · Zbl 0151.20203
[4] Birman, M. S.; Solomjak, M. Z., Piecewise polynomial approximation of functions of class \(W_p^{α\) · Zbl 0173.16001
[5] Clark, C., An embedding theorem for function spaces, Pacific J. Math., 19, 243-251 (1965) · Zbl 0141.31103
[6] Dunford, N.; Schwartz, J. T., Linear Operators I (1967), Interscience: Interscience New York
[7] Hutton, C. V.; Morell, J. S.; Retherford, J. R., Diagonal operators, approximation numbers, and Kolmogoroff diameters, J. Approximation Theory, 16, 48-80 (1976) · Zbl 0325.46028
[8] Ismagilov, R. S., Diameters of sets in normed linear spaces and the approximation of functions by trigonometric polynomials, Russian Math. Surveys, 29, 169-186 (1974) · Zbl 0303.41039
[9] Johnen, H., Über Sätze von M. Zamansky und S. B. Steckin und ihre Umkehrungen auf dem \(n\)-dimensionalen Torus, J. Approximation Theory, 2, 97-110 (1969) · Zbl 0189.35501
[10] König, H., Operator properties of Sobolev imbeddings over unbounded domains, J. Functional Analysis, 24, 32-51 (1977) · Zbl 0341.46023
[11] Pietsch, A., Nukleare lokalkonvexe Räume (1969), Verlag Akademie der Wissenschaften: Verlag Akademie der Wissenschaften Berlin · Zbl 0184.14602
[12] Pietsch, A., Theorie der Operatorenideale (1972), Universität Jena · Zbl 0238.46067
[13] Pietsch, A., \(s\)-numbers of operators in Banach spaces, Studia Math., 51, 201-223 (1974) · Zbl 0294.47018
[14] Solomjak, M. Z.; Tichomirov, V. M., On geometric characteristics of the imbedding of classes \(W_p^{α\) · Zbl 0156.36801
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