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Heat equation and the principle of not feeling the boundary

Published online by Cambridge University Press:  14 November 2011

M. van den Berg
M. van den Berg
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, Scotland, U.K.
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Synopsis

We prove a lower bound for the Dirichlet heat kernel pD(x,y;t), where x and y are a visible pair of points in an open set D in ℝm.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 112 , Issue 3-4 , 1989 , pp. 257 - 262
Copyright
Copyright © Royal Society of Edinburgh 1989

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References

1Kac, M.. On some connections between probability theory and differential and integral equations. Proc. Second Berkeley Symposium on Math. Statistics and Probability, pp. 189–215 (Berkeley, 1951).Google Scholar
2Hunt, G. A.. Some theorems concerning brownian motion. Trans. Amer. Math. Soc. 81(1956), 294–319.CrossRefGoogle Scholar
3Ciesielski, Z.. Heat conduction and the principle of not feeling the boundary. Bull. Acad. Pol. Sci., Ser. Sci. Math. Astr. Phys. 14 (1966), 435–440.Google Scholar
4Varadhan, S. R. S.. Diffusion processes in a small time interval. Comm. Pure Appl. Math. 20 (1967), 659–685.CrossRefGoogle Scholar
5Simon, B.. Classical boundary conditions as a technical tool in modern mathematics. Adv. in Math. 30 (1978), 377–385.CrossRefGoogle Scholar
6Davies, E. B.. Spectral properties of compact manifolds and change of metric (preprint, 1988).Google Scholar
7Berg, M. van den. Gaussian bounds for the Dirichlet heat kernel. J. Fund. Anal, (to appear).Google Scholar
8Berg, M. van den. On the asymptotics of the heat equation and bounds on traces associated with the Dirichlet laplacian. J. Fund. Anal. 71 (1987), 279–293.CrossRefGoogle Scholar