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A Hausdorff measure classification of polar sets for the heat equation

Published online by Cambridge University Press:  24 October 2008

S. J. Taylor  and
N. A. Watson
S. J. Taylor
Affiliation:
University of Virginia, U.S.A.
N. A. Watson
Affiliation:
University of Canterbury, New Zealand
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Extract

Our main purpose is to give criteria for determining which subsets of Rn+1 are polar relative to the heat equation

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 2 , March 1985 , pp. 325 - 344
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Besicovitch, A. S.. On the existence of subsets of finite measure of sets of infinite measure. Indag. Math. 14 (1952), 339–344.Google Scholar
[2]Carleson, L.. Selected Problems on Exceptional Sets (Van Nostrand, 1967).Google Scholar
[3]Dont, M.. On the continuity of heat potentials. Časopis Pěst. Mat. 106 (1981), 156–167.CrossRefGoogle Scholar
[4]Doob, J. L.. Classical Potential Theory and its Probabilistic Counterpart (Springer-Verlag, 1984).Google Scholar
[5]Hawkes, J.. Measures of Hausdorff type and stable processes. Mathematika 25 (1978), 202–212.CrossRefGoogle Scholar
[6]Hayman, W. K. and Kennedy, P. B.. Subharmonic Functions, vol. 1 (Academic Press, 1976).Google Scholar
[7]Kahane, J.-P.. Points multiples des processus de Lévy symétriques stables restraints à un ensemble de valeurs du temps. Seminar on Harmonic Analysis 1981–82, pp. 74–105. Publ. Math. Orsay 83, 2, Univ. Paris XI, Orsay, 1983.Google Scholar
[8]Kaufman, R. and Wu, J.-M.. Parabolic potential theory. J. Differential Equations 43 (1982), 204–234.Google Scholar
[9]Kbál, J.. Hölder-continuous heat potentials. Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 51 (1971), 17–19.Google Scholar
[10]Petrowsky, I.. Zur ersten Randwertaufgabe der Wärmeleitungsgleichung. Compositio Math. 1 (1934/1935), 383–419.Google Scholar
[11]Rogers, C. A.. Hausdorff Measures (Cambridge University Press, 1970).Google Scholar
[12]Rogers, C. A. and Taylor, S. J.. Functions continuous and singular with respect to a Hausdorff measure. Mathematika 8 (1961), 1–31.Google Scholar
[13]Taylor, S. J.. On the connexion between Hausdorff measures and generalized capacity. Proc. Cambridge Philos. Soc. 57 (1961), 524–531.Google Scholar
[14]Watson, N. A.. Green functions, potentials, and the Dirichlet problem for the heat equation. Proc. London Math. Soc. 33 (1976), 251–298;CrossRefGoogle Scholar
Corrigendum, Proc. London Math. Soc., 37 (1978), 32–34.Google Scholar
[15]Watson, N. A.. Thermal capacity. Proc. London Math. Soc. 37 (1978), 342–362.Google Scholar