Authors: Giovanni Gallavotti, Henry McKean
Boundary conditions for the heat equation in a several-dimensional
Nagoya Mathematical Journal, 47, 1-14, 1972.
The heat equation $\partial p/\partial t = \Delta p/2$ is to be solved in a several dimensional region $D$ with $\partial p = k p + j \Delta p/2$ on the boundary $B$ of $D$. The elementary solution (Green's function) is interpreted as the transition density of an associated Brownian motion. The latter is built up pathwise from the free Brownian motion by simple geometric and probabilistic transformations.
Brownian motion, Wiener integral, Images method
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