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Convergence of fundamental solutions of linear parabolic equations under Cheeger–Gromov convergence

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Abstract

In this note we show the convergence of the fundamental solutions of the parabolic equations assuming the Cheeger–Gromov convergence of the underlying manifolds and the uniform L 1-bound of the solutions. We also prove a local integral estimate of fundamental solutions.

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  1. University of Oregon, Eugene, USA

    Peng Lu

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  1. Peng Lu
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Correspondence to Peng Lu.

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Lu, P. Convergence of fundamental solutions of linear parabolic equations under Cheeger–Gromov convergence. Math. Ann. 353, 193–217 (2012). https://doi.org/10.1007/s00208-011-0679-7

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  • DOI: https://doi.org/10.1007/s00208-011-0679-7

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