Authors: Giovanni Gallavotti, Henry McKean

Title: Boundary conditions for the heat equation in a several-dimensional region
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.

Key words:  Brownian motion, Wiener integral, Images method

Giovanni Gallavotti
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