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Uniqueness of $L^p$ subsolutions to the heat equation on Finsler measure spaces
Published online by Cambridge University Press: 05 June 2023
Abstract
Let $(M, F, m)$ be a forward complete Finsler measure space. In this paper, we prove that any nonnegative global subsolution in $L^p(M)(p>1)$ to the heat equation on $\mathbb R^+\times M$ is uniquely determined by the initial data. Moreover, we give an $L^p(0<p\leq 1)$ Liouville-type theorem for nonnegative subsolutions u to the heat equation on $\mathbb R\times M$ by establishing the local $L^p$ mean value inequality for u on M with Ric$_N\geq -K(K\geq 0)$.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society
Footnotes
This paper is supported by the NNSFC (Grant No. 12071423) and the Scientific Research Foundation of HDU (Grant No. KYS075621060).