KMS Of Academy of mathematics and systems sciences, CAS
Convergence From Power-Law to Logarithm-Law in Nonlinear Scalar Field Equations | |
Wang, Zhi-Qiang1,2; Zhang, Chengxiang3 | |
2019 | |
发表期刊 | ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS |
ISSN | 0003-9527 |
卷号 | 231期号:1页码:45-61 |
摘要 | In this note, we uncover a relation between power-law nonlinear scalar field equations and logarithmic-law scalar field equations.We show that the ground state solutions, as p 2 for the power-law scalar field equations, converge to the ground state solutions of the logarithmic-law equations. As an application of this relation, we show that the associated Sobolev inequalities for imbedding from W-1,W-2(RN) into L-p (RN) converge to an associated logarithmic Sobolev inequality, giving a new proof of the latter inequality due to Lieb-Loss (Analysis, 2nd edn, Graduate studies in mathematics, 14, American Mathematical Society, Providence, 2001). Using this relation, we also derive a Liouville type theorem for positive solutions of the nonlinear scalar field equation with power-law nonlinearity, giving a sharp version of an earlier result in Felmer etal. (Ann Inst Henri Poincare Anal Non Lineaire 25(1): 105-119, 2008). |
DOI | 10.1007/s00205-018-1270-0 |
语种 | 英语 |
资助项目 | [NSFC-11771324] |
WOS研究方向 | Mathematics ; Mechanics |
WOS类目 | Mathematics, Applied ; Mechanics |
WOS记录号 | WOS:000456378100002 |
出版者 | SPRINGER |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/32332 |
专题 | 中国科学院数学与系统科学研究院 |
通讯作者 | Wang, Zhi-Qiang |
作者单位 | 1.Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China 2.Utah State Univ, Dept Math & Stat, Logan, UT 84322 USA 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
推荐引用方式 GB/T 7714 | Wang, Zhi-Qiang,Zhang, Chengxiang. Convergence From Power-Law to Logarithm-Law in Nonlinear Scalar Field Equations[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,2019,231(1):45-61. |
APA | Wang, Zhi-Qiang,&Zhang, Chengxiang.(2019).Convergence From Power-Law to Logarithm-Law in Nonlinear Scalar Field Equations.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,231(1),45-61. |
MLA | Wang, Zhi-Qiang,et al."Convergence From Power-Law to Logarithm-Law in Nonlinear Scalar Field Equations".ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 231.1(2019):45-61. |
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