Direct Methods for Pseudo-relativistic Schrodinger Operators

doi:10.1007/s12220-020-00492-1

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	Direct Methods for Pseudo-relativistic Schrodinger Operators
	Dai, Wei 1; Qin, Guolin 2,3; Wu, Dan 4
	2020-08-08
发表期刊	JOURNAL OF GEOMETRIC ANALYSIS
ISSN	1050-6926
页码	64
摘要	In this paper, we establish various maximal principles and develop the direct moving planes and sliding methods for equations involving the physically interesting (nonlocal) pseudo-relativistic Schrodinger operators (-Delta + m(2))(s) with s is an element of (0, 1) and mass m > 0. As a consequence, we also derivemultiple applications of these direct methods. For instance, we prove monotonicity, symmetry and uniqueness results for solutions to various equations involving the operators (-Delta + m(2))s in bounded or unbounded domains with certain geometrical structures (e.g., coercive epigraph and epigraph), including pseudo-relativistic Schrodinger equations, 3D boson star equations and the equations with De Giorgi-type nonlinearities. When m = 0 and s = 1, equations with De Giorgi-type nonlinearities are related to De Giorgi conjecture connected with minimal surfaces and the scalar Ginzburg-Landau functional associated to harmonic map.
关键词	Pseudo-relativistic Schrodinger operators Epigraph 3D boson star equations Direct methods of moving planes Direct sliding methods
DOI	10.1007/s12220-020-00492-1
收录类别	SCI
语种	英语
资助项目	NNSF of China[11971049] ; Fundamental Research Funds for the Central Universities ; NSFC[11901183] ; NSF of Hunan Province[2017JJ3028] ; Young Teachers Program of Hunan University[531118040104]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000557344300002
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/51953
专题	中国科学院数学与系统科学研究院
通讯作者	Wu, Dan
作者单位	1.Beihang Univ BUAA, Sch Math Sci, Beijing 100083, Peoples R China 2.Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Beijing 100049, Peoples R China 4.Hunan Univ, Coll Math, Changsha 410082, Peoples R China
推荐引用方式 GB/T 7714	Dai, Wei,Qin, Guolin,Wu, Dan. Direct Methods for Pseudo-relativistic Schrodinger Operators[J]. JOURNAL OF GEOMETRIC ANALYSIS,2020:64.
APA	Dai, Wei,Qin, Guolin,&Wu, Dan.(2020).Direct Methods for Pseudo-relativistic Schrodinger Operators.JOURNAL OF GEOMETRIC ANALYSIS,64.
MLA	Dai, Wei,et al."Direct Methods for Pseudo-relativistic Schrodinger Operators".JOURNAL OF GEOMETRIC ANALYSIS (2020):64.