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Boundary Conditions for the Heat Equation in a Several-Dimensional Region*

Published online by Cambridge University Press:  22 January 2016

G. Gallavotti  and
H. P. McKean
G. Gallavotti
Affiliation:
Universita di Roma, Roma, Italy, Courant Institute of Mathematical Sciences, New York University, New York, U.S.A.
H. P. McKean
Affiliation:
Universita di Roma, Roma, Italy, Courant Institute of Mathematical Sciences, New York University, New York, U.S.A.
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Abstract

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The heat equation is to be solved in a severaldimensional region D with 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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 47 , September 1972 , pp. 1 - 14
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

Footnotes

*

The work of the second author was supported in part by the Office of Naval Research, Contract N00014-67-A-0467-0014. Reproduction in whole or in part is permitted for any purpose of the United States Government.

References

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