{"title":"Finsler测度空间上热方程亚解的唯一性","authors":"Qiaoling Xia","doi":"10.4153/s0008439523000450","DOIUrl":null,"url":null,"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 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).","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Uniqueness of subsolutions to the heat equation on Finsler measure spaces\",\"authors\":\"Qiaoling Xia\",\"doi\":\"10.4153/s0008439523000450\",\"DOIUrl\":null,\"url\":null,\"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 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).\",\"PeriodicalId\":55280,\"journal\":{\"name\":\"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-06-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4153/s0008439523000450\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4153/s0008439523000450","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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).
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The Canadian Mathematical Bulletin was established in 1958 to publish original, high-quality research papers in all branches of mathematics and to accommodate the growing demand for shorter research papers. The Bulletin is a companion publication to the Canadian Journal of Mathematics that publishes longer papers. New research papers are published continuously online and collated into print issues four times each year.
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