Qualitative properties of singular solutions to fractional elliptic equations

doi:10.1017/prm.2021.52

	Qualitative properties of singular solutions to fractional elliptic equations
	Huang, Shuibo 5,6; Zhang, Zhitao 2,3,4; Liu, Zhisu 1
刊名	PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
	2021-09-14
页码	36
关键词	Fractional elliptic equations Moving spheres method Blow-up analysis Local behaviour Singular solutions
ISSN号	0308-2105
DOI	10.1017/prm.2021.52
英文摘要	In this paper, by the moving spheres method, Caffarelli-Silvestre extension formula and blow-up analysis, we study the local behaviour of nonnegative solutions to fractional elliptic equations (-Delta)(alpha)u = f(u), x is an element of Omega\Gamma, where 0 < alpha < 1, Omega = R-N or Omega is a smooth bounded domain, Gamma is a singular subset of n with fractional capacity zero, f (t) is locally bounded and positive for t is an element of [0, infinity), and f (t)/t((N+2 alpha)/(N-2 alpha)) is nonincreasing in t for large t, rather than for every t > 0. Our main result is that the solutions satisfy the estimate f(u(x))/u(x) <= Cd(x, Gamma)(-2 alpha). This estimate is new even for Gamma = {0}. As applications, we derive the spherical Harnack inequality, asymptotic symmetry, cylindrical symmetry of the solutions.
资助项目	National Natural Science Foundation of China[11701267] ; National Natural Science Foundation of China[11761059] ; National Natural Science Foundation of China[11771428] ; National Natural Science Foundation of China[12026217] ; National Natural Science Foundation of China[12031015] ; Program for Yong Talent of State Ethnic Affairs Commission of China[XBMU-2019-AB-34] ; Innovation Team Project of Northwest Minzu University[1110130131] ; First-Rate Discipline of Northwest Minzu University ; Hunan Natural Science Excellent Youth Fund[2020JJ3029] ; Fundamental Research Funds for the Central Universities ; China University of Geosciences[CUG2106211] ; China University of Geosciences[CUGST2]
WOS研究方向	Mathematics
语种	英语
出版者	CAMBRIDGE UNIV PRESS
WOS记录号	WOS:000785643100001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60334]
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Zhitao
作者单位	1.China Univ Geosci, Ctr Math Sci, Wuhan 430074, Hubei, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Acad Math & Syst Sci, Chinese Acad Sci, HLM, Beijing 100190, Peoples R China 4.Jiangsu Univ, Sch Math Sci, Zhenjiang 212013, Jiangsu, Peoples R China 5.Northwest Minzu Univ, Key Lab Streaming Data Comp Technol & Applicat, Lanzhou 730030, Gansu, Peoples R China 6.Northwest Minzu Univ, Sch Math & Comp Sci, Lanzhou 730030, Gansu, Peoples R China
推荐引用方式 GB/T 7714	Huang, Shuibo,Zhang, Zhitao,Liu, Zhisu. Qualitative properties of singular solutions to fractional elliptic equations[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS,2021:36.
APA	Huang, Shuibo,Zhang, Zhitao,&Liu, Zhisu.(2021).Qualitative properties of singular solutions to fractional elliptic equations.PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS,36.
MLA	Huang, Shuibo,et al."Qualitative properties of singular solutions to fractional elliptic equations".PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS (2021):36.