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

G. Gallavotti; H. P. McKean

doi:10.1017/s0027763000014872

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

G. Gallavotti, H. P. McKean

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The heat equation ∂p/∂t = Δp/2 is to be solved in a severaldimensional region D with ∂p = ∂p + jΔp/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.

Original language	English (US)
Pages (from-to)	1-14
Number of pages	14
Journal	Nagoya Mathematical Journal
Volume	47
DOIs	https://doi.org/10.1017/s0027763000014872
State	Published - 1972

ASJC Scopus subject areas

General Mathematics

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10.1017/s0027763000014872

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

Abstract

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