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Uniqueness of
$L^p$ subsolutions to the heat equation on Finsler measure spaces
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 67 / Issue 1 / March 2024
- Published online by Cambridge University Press:
- 05 June 2023, pp. 166-175
- Print publication:
- March 2024
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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
$_N\geq -K(K\geq 0)$.
