### 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 |

State | Published - 1972 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Nagoya Mathematical Journal*,

*47*, 1-14.

**Boundary conditions for the heat equation in a several-dimensional region.** / Gallavotti, G.; McKean, H. P.

Research output: Contribution to journal › Article

*Nagoya Mathematical Journal*, vol. 47, pp. 1-14.

}

TY - JOUR

T1 - Boundary conditions for the heat equation in a several-dimensional region

AU - Gallavotti, G.

AU - McKean, H. P.

PY - 1972

Y1 - 1972

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84972529985&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972529985&partnerID=8YFLogxK

M3 - Article

VL - 47

SP - 1

EP - 14

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

SN - 0027-7630

ER -