Abstract
We provide sharp two-sided estimates on the Dirichlet heat kernel k1(t, x, y) for the Laplacian in a ball. The result accurately describes the exponential behaviour of the kernel for small times and significantly improves the qualitatively sharp results known so far. As a consequence we obtain the full description of the kernel k1(t, x, y) in terms of its global two-sided sharp estimates. Such precise estimates were possible to obtain due to the enrichment of analytical methods with probabilistic tools.
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Jacek Małecki was supported by the National Science Centre grant no. 2013/11/D/ST1/02622. Grzegorz Serafin was financed by the National Science Centre grant no. 2015/18/E/ST1/00239.
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Małecki, J., Serafin, G. Dirichlet Heat Kernel for the Laplacian in a Ball. Potential Anal 52, 545–563 (2020). https://doi.org/10.1007/s11118-018-9750-2
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DOI: https://doi.org/10.1007/s11118-018-9750-2