Qualitative properties of singular solutions to fractional elliptic equations
文献类型：期刊论文
| 作者 | Huang, Shuibo5,6; Zhang, Zhitao2,3,4; Liu, Zhisu1 |
| 刊名 | PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
 |
| 出版日期 | 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 |
| WOS记录号 | WOS:000785643100001 |
| 出版者 | CAMBRIDGE UNIV PRESS |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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