Skip to main content Accessibility help

Heat equation and the principle of not feeling the boundary

  • M. van den Berg (a1)


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.



Hide All
1Kac, M.. On some connections between probability theory and differential and integral equations. Proc. Second Berkeley Symposium on Math. Statistics and Probability, pp. 189215 (Berkeley, 1951).
2Hunt, G. A.. Some theorems concerning brownian motion. Trans. Amer. Math. Soc. 81(1956), 294319.
3Ciesielski, Z.. Heat conduction and the principle of not feeling the boundary. Bull. Acad. Pol. Sci., Ser. Sci. Math. Astr. Phys. 14 (1966), 435440.
4Varadhan, S. R. S.. Diffusion processes in a small time interval. Comm. Pure Appl. Math. 20 (1967), 659685.
5Simon, B.. Classical boundary conditions as a technical tool in modern mathematics. Adv. in Math. 30 (1978), 377385.
6Davies, E. B.. Spectral properties of compact manifolds and change of metric (preprint, 1988).
7Berg, M. van den. Gaussian bounds for the Dirichlet heat kernel. J. Fund. Anal, (to appear).
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), 279293.


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed