Results on entire solutions for a degenerate critical elliptic equation with anisotropic coefficients

doi:10.1007/s11425-010-4118-0

CSpace

	Results on entire solutions for a degenerate critical elliptic equation with anisotropic coefficients
	Chen ShaoWei 2; Lin LiShan 1
	2011-02-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	54 期号:2 页码:221-242
摘要	In this paper, we study the following degenerate critical elliptic equation with anisotropic coefficients -duv(vertical bar x(N)vertical bar(2 alpha)del u) = K(x)vertical bar x(N)vertical bar(alpha.2)((s)) (s)vertical bar u vertical bar(2)((s)) (2)u in R(N), where x = (x1, ... , x(N)) is an element of R(N), N >= 3, alpha > 1/2, 0 <= s <= 2 and 2* (s) = 2(N - s)/(N - 2). Some basic properties of the degenerate elliptic operator -div(vertical bar x(N)vertical bar(2 alpha a)del u) are investigated and some regularity, symmetry and uniqueness results for entire solutions of this equation are obtained. We also get some variational identities for solutions of this equation. As consequences, we obtain some nonexistence results for this equation.
关键词	weighted Sobolev inequalities Harnack inequality moving sphere method variational identities
DOI	10.1007/s11425-010-4118-0
语种	英语
资助项目	National Natural Science Foundation of China[10901112] ; National Natural Science Foundation of China[11001255] ; Beijing Natural Science Foundation[1102013] ; China Postdoctoral Science Foundation[20090460548]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000287200600002
出版者	SCIENCE CHINA PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11418
专题	中国科学院数学与系统科学研究院
通讯作者	Lin LiShan
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China 2.Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China
推荐引用方式 GB/T 7714	Chen ShaoWei,Lin LiShan. Results on entire solutions for a degenerate critical elliptic equation with anisotropic coefficients[J]. SCIENCE CHINA-MATHEMATICS,2011,54(2):221-242.
APA	Chen ShaoWei,&Lin LiShan.(2011).Results on entire solutions for a degenerate critical elliptic equation with anisotropic coefficients.SCIENCE CHINA-MATHEMATICS,54(2),221-242.
MLA	Chen ShaoWei,et al."Results on entire solutions for a degenerate critical elliptic equation with anisotropic coefficients".SCIENCE CHINA-MATHEMATICS 54.2(2011):221-242.