Dirichlet Heat Kernel for the Laplacian in a Ball
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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.
KeywordsLaplacian Ball Heat kernel Estimates Exit time
Mathematics Subject Classification (2010)35K08 60J65
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