LIOUVILLE TYPE RESULTS AND REGULARITY OF THE EXTREMAL SOLUTIONS OF BIHARMONIC EQUATION WITH NEGATIVE EXPONENTS
被引:23
作者:
Guo, Zongming
论文数: 0引用数: 0
h-index: 0
机构:
Henan Normal Univ, Dept Math, Xinxiang 453007, Peoples R ChinaHenan Normal Univ, Dept Math, Xinxiang 453007, Peoples R China
Guo, Zongming
[1
]
Wei, Juncheng
论文数: 0引用数: 0
h-index: 0
机构:
Univ Hong Kong, Dept Math Chinese, Shatin, Hong Kong, Peoples R China
Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, CanadaHenan Normal Univ, Dept Math, Xinxiang 453007, Peoples R China
Wei, Juncheng
[2
,3
]
机构:
[1] Henan Normal Univ, Dept Math, Xinxiang 453007, Peoples R China
[2] Univ Hong Kong, Dept Math Chinese, Shatin, Hong Kong, Peoples R China
[3] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada
Stable entire solutions;
biharmonic equations with singularity;
regularity of the extremal solutions;
POSITIVE SOLUTIONS;
ELLIPTIC EQUATION;
STABLE-SOLUTIONS;
COMPACTNESS;
STABILITY;
D O I:
10.3934/dcds.2014.34.2561
中图分类号:
O29 [应用数学];
学科分类号:
070104 ;
摘要:
We first obtain Liouville type results for stable entire solutions of the biharmonic equation -Delta(2)u = u(-p) in R-N for p > 1 and 3 <= N <= 12. Then we consider the Navier boundary value problem for the corresponding equation and improve the known results on the regularity of the extremal solution for 3 <= N <= 12. As a consequence, in the case of p = 2, we show that the extremal solution u* is regular when N = 7. This improves earlier results of Guo-Wei [20] (N <= 4), Cowan-Esposito-Ghoussoub [2] (N = 5), Cowan-Ghoussoub [4] (N = 6).