KMS Of Academy of mathematics and systems sciences, CAS
Results on entire solutions for a degenerate critical elliptic equation with anisotropic coefficients | |
Chen ShaoWei2; Lin LiShan1 | |
2011-02-01 | |
Source Publication | SCIENCE CHINA-MATHEMATICS |
ISSN | 1674-7283 |
Volume | 54Issue:2Pages:221-242 |
Abstract | 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. |
Keyword | weighted Sobolev inequalities Harnack inequality moving sphere method variational identities |
DOI | 10.1007/s11425-010-4118-0 |
Language | 英语 |
Funding Project | 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 Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000287200600002 |
Publisher | SCIENCE CHINA PRESS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/11418 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Lin LiShan |
Affiliation | 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 |
Recommended Citation 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. |
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