### 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 |

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### Keywords

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

### Cite this

*Probability Theory and Related Fields*,

*100*(4), 439-456. https://doi.org/10.1007/BF01268989

}

*Probability Theory and Related Fields*, vol. 100, no. 4, pp. 439-456. https://doi.org/10.1007/BF01268989

**Heat content and Brownian motion for some regions with a fractal boundary.** / van den Berg, M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Heat content and Brownian motion for some regions with a fractal boundary

AU - van den Berg, M.

PY - 1994/12

Y1 - 1994/12

N2 - Let D be an open, bounded set in euclidean space Rm (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 ED(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.

AB - Let D be an open, bounded set in euclidean space Rm (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 ED(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.

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

UR - http://www.scopus.com/inward/record.url?scp=21844497691&partnerID=8YFLogxK

U2 - 10.1007/BF01268989

DO - 10.1007/BF01268989

M3 - Article

VL - 100

SP - 439

EP - 456

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 4

ER -