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GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR LICHNEROWICZ EQUATIONS

文献类型：期刊论文

作者Huang, Pingliang1; Wang, Youde2,3,4
刊名PACIFIC JOURNAL OF MATHEMATICS
出版日期2022-04-01
卷号317期号:2页码:363-386
关键词gradient estimate Ricci curvature Liouville theorem Harnack inequality nonlinear elliptic equations
ISSN号0030-8730
DOI10.2140/pjm.2022.317.363
英文摘要We study the positive solutions to a class of general semilinear elliptic equations Delta u(x) + uh(ln u) = 0 defined on a complete Riemannian manifold (M, g) with Ric(g) >= -K g, and obtain Li-Yau-type gradient estimates of positive solutions to these equations which do not depend on the bounds of the solutions or the Laplacian of the distance function on (M, g). We also obtain some Liouville-type theorems for these equations when (M, g) is non-compact and Ric(g) >= 0 and establish some Harnack inequalities as consequences. As applications of the main theorem, we extend our techniques to the Lichnerowicz-type equations Delta u+lambda(1)u+lambda(2)u ln u+lambda(3)u(b+1)+lambda(4)u(p+1) = 0, the Einstein-scalar field Lichnerowicz equations Delta u+lambda(1)u+lambda(2)u(b+1)+lambda(3)u(p+1) = 0 with dim M >= 3 and the two-dimensional Einstein-scalar field Lichnerowicz equation Delta u + Ae(2u) + Be-2u + D = 0, and obtain some similar gradient estimates and Liouville theorems under some suitable analysis conditions on these equations.
资助项目NSFC[11731001] ; NSFC[11971400] ; NSFC[2020YFA0712500] ; Guangdong Basic and Applied Basic Research Foundation[2020A1515011019]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000830310400015
出版者MATHEMATICAL SCIENCES PUBLISHERS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/61145]  
专题中国科学院数学与系统科学研究院
通讯作者Huang, Pingliang
作者单位1.Shanghai Univ, Dept Math, Shanghai, Peoples R China
2.Guangzhou Univ, Sch Math & Informat Sci, Guangzhou, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Hua Loo Keng Key Lab Math, Beijing, Peoples R China
4.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
推荐引用方式
GB/T 7714		 Huang, Pingliang,Wang, Youde. GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR LICHNEROWICZ EQUATIONS[J]. PACIFIC JOURNAL OF MATHEMATICS,2022,317(2):363-386.
APA Huang, Pingliang,&Wang, Youde.(2022).GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR LICHNEROWICZ EQUATIONS.PACIFIC JOURNAL OF MATHEMATICS,317(2),363-386.
MLA Huang, Pingliang,et al."GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR LICHNEROWICZ EQUATIONS".PACIFIC JOURNAL OF MATHEMATICS 317.2(2022):363-386.

入库方式： OAI收割

来源：数学与系统科学研究院

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