Moser-Trudinger inequality involving the anisotropic Dirichlet norm ( integral(Omega) F-N (del u)dx)1/N on W-0(-1),N (Omega)
Moser-Trudinger inequality involving the anisotropic Dirichlet norm ( integral(Omega) F-N (del u)dx)1/N on W-0(-1),N (Omega)
复制标题
涉及各向异性狄利克雷范数的 Moser-Trudinger 不等式 (积分(Omega) F-N (del u)dx)1/N on W-0(-1),N (Omega)
DOI：
10.1016/j.jfa.2018.12.001
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发表时间：
2019
影响因子：
1.7
通讯作者：
Zhou Chunqin
中科院分区：
文献类型：
--
作者：
Zhou Changliang;Zhou Chunqin
研究了一个涉及各向异性Dirichlet范数（<$Ω FN（<$u）dx）1 N在W 0 1，N（Ω）（N≥ 2）上的尖锐的Moser-Trudinger不等式.这里F是凸齐次的，它的极函数Fo表示RN上的Finsler度量.在这种各向异性的Dirichlet范数下，我们建立了Lions型集中紧性替代。然后利用Blow-up方法，得到了这个尖锐几何不等式极值函数的存在性。
We investigate a sharp Moser–Trudinger inequality which involves the anisotropic Dirichlet norm (∫ Ω F N (∇ u) d x) 1 N on W 0 1, N (Ω) for N≥ 2. Here F is convex and homogeneous of degree 1, and its polar F o represents a Finsler metric on R N. Under this anisotropic Dirichlet norm, we establish the Lions type concentration-compactness alternative. Then by using a blow-up procedure, we obtain the existence of extremal functions for this sharp geometric inequality.