Heat flow, Brownian motion and Newtonian capacity |
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Authors: | M van den Berg |
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Institution: | School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom |
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Abstract: | Let K be a compact, non-polar set in Rm(m?3) and let u be the unique weak solution of on Rm\K×(0,∞),u(x;0)=0 on Rm\K and u(x;t)=1 for all x on the boundary of K and for all t>0. The asymptotic behaviour of u(x;t) as t tends to infinity is obtained up to order O(t−m/2). |
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Keywords: | 35K20 60J65 60J45 |
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