Geodesic
Note on the Support of Sobolev Functions
Canadian mathematical bulletin, Tome 41 (1998) no. 3, pp. 257-260

Voir la notice de l'article provenant de la source Cambridge University Press

We prove a topological restriction on the support of Sobolev functions.
DOI : 10.4153/CMB-1998-037-4
Mots-clés : 46E35, 31B05, Sobolev spaces, harmonic approximation 
Bagby, Thomas; Gauthier, P. M. Note on the Support of Sobolev Functions. Canadian mathematical bulletin, Tome 41 (1998) no. 3, pp. 257-260. doi: 10.4153/CMB-1998-037-4
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[AH] [AH] Adams, D. R. and Hedberg, L. I., Function Spaces and Potential Theory. Springer-Verlag, New York, Berlin, Heidelberg, 1996. Google Scholar

[BCG] [BCG] Bagby, T., Cornea, A., and Gauthier, P. M., Harmonic approximation on arcs. Constr. Approx. 9 (1993), 501–507. Google Scholar

[EG] [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] [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] [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] [H] Hedberg, L. I., Approximation by harmonic functions, and stability of the Dirichlet problem. Exposition. Math. 11 (1993), 193–259. Google Scholar

[I] [I] Iversen, B., Cohomology of Sheaves. Springer-Verlag, New York, Heidelberg, Berlin, 1986. Google Scholar

[L] [L] Landkof, N. S., Foundations of Modern Potential Theory. Springer-Verlag, New York, Heidelberg, Berlin, 1972. Google Scholar

[M] [M] Meyers, N. G., Continuity of Bessel potentials. Israel J. Math. 11 (1972), 271–283. Google Scholar

[Mo] [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] [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] [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

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