**Authors**: Giovanni
Gallavotti, Henry McKean

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

Nagoya Mathematical Journal, ** 47**, 1-14, 1972.

**Abstract:**

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

Fisica, Universita' di Roma 1

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