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Thinness and boundary behaviour of potentials for the heat equation

  • N. A. Watson (a1)

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For (x, t) ∈ Rn+1, we put

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