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

M. van den Berg

doi:10.1007/BF01268989

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

M. van den Berg

School of Mathematical & Computer Sciences

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

26 Citations (Scopus)

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
Pages (from-to)	439-456
Number of pages	18
Journal	Probability Theory and Related Fields
Volume	100
Issue number	4
DOIs	https://doi.org/10.1007/BF01268989
Publication status	Published - Dec 1994

Keywords

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

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10.1007/BF01268989

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

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DO - 10.1007/BF01268989

M3 - Article

SN - 0178-8051

VL - 100

SP - 439

EP - 456

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 4

ER -

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

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Keywords

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