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Note on the Support of Sobolev Functions

Published online by Cambridge University Press:  20 November 2018

Thomas Bagby  and
P. M. Gauthier
Thomas Bagby
Affiliation:
Department of Mathematics Rawles Hall Indiana University Bloomington, Indiana 47405 U.S.A.
P. M. Gauthier
Affiliation:
Département de mathématiques et de statistique et Centre de recherches mathématiques, Université de Montréal CP 6128 Centreville Montréal, Québec H3C 3J7
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Abstract

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We prove a topological restriction on the support of Sobolev functions.

Keywords

46E3531B05Sobolev spacesharmonic approximation
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 3 , 01 September 1998 , pp. 257 - 260
Copyright
Copyright © Canadian Mathematical Society 1998

References

[AH] Adams, D. R. and Hedberg, L. I., Function Spaces and Potential Theory. Springer-Verlag, New York, Berlin, Heidelberg, 1996.Google Scholar
[BCG] Bagby, T., Cornea, A., and Gauthier, P. M., Harmonic approximation on arcs. Constr. Approx. 9 (1993), 501–507.Google Scholar
[EG] Evans, L. C. and Gariepy, R. F., Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton, Ann Arbor, London, 1992.Google Scholar
[GH] Gauthier, P. M. and Hengartner, W., Approximation Uniforme Qualitative sur des Ensembles Non Bornés. Les Presses de l’Université de Montréal, 1982.Google Scholar
[GZ] Goffman, C. and Ziemer, W. P., Higher dimensional mappings for which the area formula holds. Ann. of Math. 92 (1970), 482–488.Google Scholar
[H] Hedberg, L. I., Approximation by harmonic functions, and stability of the Dirichlet problem. Exposition. Math. 11 (1993), 193–259.Google Scholar
[I] Iversen, B., Cohomology of Sheaves. Springer-Verlag, New York, Heidelberg, Berlin, 1986.Google Scholar
[L] Landkof, N. S., Foundations of Modern Potential Theory. Springer-Verlag, New York, Heidelberg, Berlin, 1972.Google Scholar
[M] Meyers, N. G., Continuity of Bessel potentials. Israel J. Math. 11 (1972), 271–283.Google Scholar
[Mo] Moore, R. L., Concerning triods in the plane and the junction points of plane continua. Proc. Nat. Acad. Sci. U.S.A. 14 (1928), 85–88.Google Scholar
[P] Polking, J. C., A Leibniz formula for some differentiation operators of fractional order. Indiana Univ. Math. J. 21 (1972), 1019–1029.Google Scholar
[W] Walsh, J. L., The approximation of harmonic functions by harmonic polynomials and by harmonic rational functions. Bull. Amer.Math. Soc. 35 (1929), 499–544.Google Scholar