Poisson’s integral formula via heat kernels
Keyword(s):
Abstract We give another proof of Poisson’s integral formula for harmonic functions in a ball or a half space by using heat kernels with Green’s formula. We wish to emphasize that this method works well even for a half space, which is an unbounded domain; the functions involved are integrable, since the heat kernel decays rapidly. This method needs no trick such as the subordination identity, which is indispensable when applying the Fourier transform method for a half space.
2006 ◽
Vol 306-308
◽
pp. 1223-1228
1986 ◽
Vol 21
(5)
◽
pp. 587-593
◽
2011 ◽
Vol 112
(2)
◽
pp. 414-425
◽
2000 ◽
Vol 48
(7)
◽
pp. 1025-1032
◽