Uniqueness of $L^p$ subsolutions to the heat equation on Finsler measure spaces
Canadian mathematical bulletin, Tome 67 (2024) no. 1, pp. 166-175
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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 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$_N\geq -K(K\geq 0)$.
Mots-clés :
Finsler measure space, weighted Ricci curvature, heat equation, mean value inequality
Xia, Qiaoling. Uniqueness of $L^p$ subsolutions to the heat equation on Finsler measure spaces. Canadian mathematical bulletin, Tome 67 (2024) no. 1, pp. 166-175. doi: 10.4153/S0008439523000450
@article{10_4153_S0008439523000450,
author = {Xia, Qiaoling},
title = {Uniqueness of $L^p$ subsolutions to the heat equation on {Finsler} measure spaces},
journal = {Canadian mathematical bulletin},
pages = {166--175},
year = {2024},
volume = {67},
number = {1},
doi = {10.4153/S0008439523000450},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000450/}
}
TY - JOUR AU - Xia, Qiaoling TI - Uniqueness of $L^p$ subsolutions to the heat equation on Finsler measure spaces JO - Canadian mathematical bulletin PY - 2024 SP - 166 EP - 175 VL - 67 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000450/ DO - 10.4153/S0008439523000450 ID - 10_4153_S0008439523000450 ER -
%0 Journal Article %A Xia, Qiaoling %T Uniqueness of $L^p$ subsolutions to the heat equation on Finsler measure spaces %J Canadian mathematical bulletin %D 2024 %P 166-175 %V 67 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000450/ %R 10.4153/S0008439523000450 %F 10_4153_S0008439523000450
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