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On heat capacity and parabolic measure

Published online by Cambridge University Press:  24 October 2008

Jang-Mei Wu
Jang-Mei Wu
Affiliation:
Department of Mathematics, University of Illinois, Urbana, IL 61801, USA
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Extract

Unlike their counterparts for the Laplace's equation, the known results on heat capacity and parabolic measure are rather incomplete. We make a few comments on these two areas.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 1 , July 1987 , pp. 163 - 172
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

REFERENCES

[1] Hawkes, J.. Polar sets, regular points and recurrent sets for the symmetric and increasing stable process. Bull. London Math. Soc. 2 (1970), 53–59.CrossRefGoogle Scholar
[2] Kaufman, R. and Wu, J.-M.. Parabolic potential theory. J. Differential Equations 43 (1982), 204–234.CrossRefGoogle Scholar
[3] Kaufman, R. and Wu, J.-M.. Parabolic measure on domains of class Lip 1/2. Preprint.Google Scholar
[4] Landkof, N. S.. Foundations of Modern Potential Theory (Springer-Verlag, 1972).CrossRefGoogle Scholar
[5] Moser, J.. A Harnack inequality for parabolic differential equations. Comm. Pure Appl. Math. 17 (1964), 101–134.CrossRefGoogle Scholar
[6] Orey, S.. Polar sets for processes with stationary independent increments. Proceedings of the Madison Symposium on Markov Processes and Potential Theory, edited by Chover, J. (J. Wiley, 1967), 117–126.Google Scholar
[7] Petrowsky, I. G.. Zur ersten Randwertaufgaben der Warmeleitungsgleichung. Compositio Math. 1 (1935), 383–419.Google Scholar
[8] Taylor, S. J. and Watson, N. A.. A Hausdorff measure classification of polar sets for the heat equation. Math. Proc. Cambridge Philos. Soc. 97 (1985), 325–344.CrossRefGoogle Scholar
[9] Watson, N. A.. Green functions, potentials, and the Dirichlet problem for the heat equation. Proc. London Math. Soc. (3) 33 (1976), 251–298.CrossRefGoogle Scholar
[10] Watson, N. A.. Thermal capacity. Proc. London Math. Soc. (3) 37 (1978), 342–362.CrossRefGoogle Scholar
[11] Wu, J.-M.. On parabolic measures and subparabolic functions. Trans. Amer. Math. Soc. 251 (1979), 171–185.CrossRefGoogle Scholar
[12] Zygmund, A.. Trigonometric Series. Vol. I, 2nd ed. (Cambridge University Press, 1959).Google Scholar