Uniqueness of L-p subsolutions to the heat equation on Finsler measure spaces

]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 R+ x M is uniquely determined by the initial data. Moreover, we give an L-p(0 < p <= 1) Liouville-type theorem for nonnegative subsolutions u to the heat equation on R x M by establishing the local Lp mean value inequality for u on M with RicN >= - K(K >= 0).

Automated summary

In this paper, it is proved that in a forward complete Finsler measure space, any nonnegative global subsolution u in L-p(M)(p > 1) to the heat equation on R+ x M is uniquely determined by the initial data. Moreover, a Liouville-type theorem for nonnegative subsolutions u to the heat equation on R x M is given by establishing the local Lp mean value inequality for u on M with RicN >= - K(K >= 0).