GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR LICHNEROWICZ EQUATIONS

doi:10.2140/pjm.2022.317.363

	GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR LICHNEROWICZ EQUATIONS
	Huang, Pingliang 1; Wang, Youde 2,3,4
刊名	PACIFIC JOURNAL OF MATHEMATICS
	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
DOI	10.2140/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
出版者	MATHEMATICAL SCIENCES PUBLISHERS
WOS记录号	WOS:000830310400015
内容类型	期刊论文
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.