### Abstract

Let D be an open, bounded set in euclidean space R^{m} (m=2, 3, ...) with boundary ?D. Suppose D has temperature 0 at time t=0, while ?D is kept at temperature 1 for all t>0. We use brownian motion to obtain estimates for the solution of corresponding heat equation and to obtain results for the asymptotic behaviour of E_{D}(t), the amount of heat in D at time t, as t?0^{+}. For the triadic von Koch snowflake K our results imply that {Mathematical expression} for some constant c>1. © 1994 Springer-Verlag.

Original language | English |
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Pages (from-to) | 439-456 |

Number of pages | 18 |

Journal | Probability Theory and Related Fields |

Volume | 100 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 1994 |

### Keywords

- Mathematics Subject Classification: 60J45, 60J60, 60J65, 35K05

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## Cite this

van den Berg, M. (1994). Heat content and Brownian motion for some regions with a fractal boundary.

*Probability Theory and Related Fields*,*100*(4), 439-456. https://doi.org/10.1007/BF01268989