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Thinness and boundary behaviour of potentials for the heat equation

Published online by Cambridge University Press:  26 February 2010

N. A. Watson
Affiliation:
Department of Mathematics, University of Canterbury, Christchurch, New Zealand.
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Extract

For (x, t) ∈ Rn+1, we put

Type
Research Article
Copyright
Copyright © University College London 1985

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References

1.Brelot, M.. On Topologies and Boundaries in Potential Theory (Springer, 1971).CrossRefGoogle Scholar
2.Deny, J.. Un théorème sur les ensembles effilés. Ann. Univ. Grenoble Sect. Sci. Math. Phys., 23 (1948), 139142.Google Scholar
3.Doob, J. L.. Classical Potential Theory and its Probabilistic Counterpart (Springer, 1984).CrossRefGoogle Scholar
4.Evans, L. C. and Gariepy, R. F.. Wiener's criterion for the heat equation. Arch. Rational Mech. Anal., 78 (1982), 293314.CrossRefGoogle Scholar
5.Hansen, W.. Fegen und Dünnheit mit Anwendungen auf die Laplace-und Wärmeleitungsgleichung. Ann. Inst. Fourier, Grenoble, 21 (1971), 79121.CrossRefGoogle Scholar
6.Kaufman, R. and Wu, J.-M.. Parabolic potential theory. J. Differential Equations, 43 (1982), 204234.CrossRefGoogle Scholar
7.Korányi, A. and Taylor, J. C.. Fine convergence and parabolic convergence for the Helmholtz equation and the heat equation. Illinois J. Math., 27 (1983), 7793.CrossRefGoogle Scholar
8.Netuka, I.. Thinness and the heat equation. Časopis Pěst. Mat, 99 (1974), 293299.CrossRefGoogle Scholar
9.Taylor, S. J. and Watson, N. A.. A Hausdorff measure classification of polar sets for the heat equation. Math. Proc. Cambridge Phil. Soc, 97 (1985), 325344.CrossRefGoogle Scholar
10.Watson, N. A.. Thermal capacity. Proc. London Math. Soc, 37 (1978), 342362.CrossRefGoogle Scholar