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

G. Gallavotti, H. P. McKean

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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 languageEnglish (US)
Pages (from-to)1-14
Number of pages14
JournalNagoya Mathematical Journal
Volume47
StatePublished - Jan 1 1972

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ASJC Scopus subject areas

  • Mathematics(all)

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