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Asymptotics for Functions Associated with Heat Flow on the Sierpinski Carpet

  Published:2010-11-06
 Printed: Feb 2011
  • B. M. Hambly,
    Mathematical Institute, University of Oxford, Oxford, U.K.
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Abstract

We establish the asymptotic behaviour of the partition function, the heat content, the integrated eigenvalue counting function, and, for certain points, the on-diagonal heat kernel of generalized Sierpinski carpets. For all these functions the leading term is of the form $x^{\gamma}\phi(\log x)$ for a suitable exponent $\gamma$ and $\phi$ a periodic function. We also discuss similar results for the heat content of affine nested fractals.
MSC Classifications: 35K05, 28A80, 35B40, 60J65 show english descriptions Heat equation
Fractals [See also 37Fxx]
Asymptotic behavior of solutions
Brownian motion [See also 58J65]
35K05 - Heat equation
28A80 - Fractals [See also 37Fxx]
35B40 - Asymptotic behavior of solutions
60J65 - Brownian motion [See also 58J65]
 

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