Asymptotic behavior of least energy solutions of a biharmonic equation in dimension four
Asymptotic behavior of least energy solutions of a biharmonic equation in dimension four
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四维双调和方程最小能量解的渐近行为
DOI：
10.1512/iumj.2006.55.2723
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发表时间：
2006
影响因子：
1.1
通讯作者：
M. Grossi
中科院分区：
文献类型：
--
作者：
M. Ayed;K. Mehdi;M. Grossi
本文考虑了R4中有界区域上非线性项具有大指数的双调和方程。我们研究了通过极小化适当的泛函得到的正解的渐近性态。其中，我们证明了当p → +∞时，非线性指数为p的能量泛函的最小值cp与ρ 4 e/p相似，其中ρ 4 = 32ω 4，ω 4为R4中单位球面S3的面积.利用这个结果，我们计算了当p → +∞时最小能量解的L ∞ -范数的极限.我们还表明，这样的解决方案爆破恰好在一个点，这是一个关键点的罗宾功能。
In this paper we consider a biharmonic equation on a bounded domain in R 4 with large exponent in the nonlinear term. We study asymptotic behavior of positive solutions obtained by minimizing suitable functionals. Among other results, we prove that c p , the minimum of energy functional with the nonlinear exponent equal to p, is like ρ 4 e/p as p → +∞, where ρ 4 = 32ω 4 and ω 4 is the area of the unit sphere S 3 in R 4 . Using this result, we compute the limit of the L ∞ -norm of least energy solutions as p → +∞. We also show that such solutions blow up at exactly one point which is a critical point of the Robin function.