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Convergence From Power-Law to Logarithm-Law in Nonlinear Scalar Field Equations
Wang, Zhi-Qiang1,2; Zhang, Chengxiang3
2019
Source PublicationARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
ISSN0003-9527
Volume231Issue:1Pages:45-61
AbstractIn 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).
DOI10.1007/s00205-018-1270-0
Language英语
Funding Project[NSFC-11771324]
WOS Research AreaMathematics ; Mechanics
WOS SubjectMathematics, Applied ; Mechanics
WOS IDWOS:000456378100002
PublisherSPRINGER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32332
Collection中国科学院数学与系统科学研究院
Affiliation1.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
Recommended Citation
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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