Finsler测度空间上热方程亚解的唯一性

Pub Date : 2023-06-05 DOI:10.4153/s0008439523000450

Qiaoling Xia

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引用次数: 0

摘要

设（M，F，M）是一个前向完全Finsler测度空间。本文证明了R+×M上热方程在Lp（M）（p>1）中的任何非负全局亚解都是由初始数据唯一确定的。此外，我们通过建立Ric N≥−K（K≥0）的M上u的局部Lp均值不等式，给出了R×M上热方程非负亚解u的Lp（0本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Uniqueness of 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 + × 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 × M by establishing the local L p mean value inequality for u on M with Ric N ≥ − K ( K ≥ 0).