论文标题
Hardy和Poincaré不平等现象
Hardy and Poincaré inequalities in fractional Orlicz-Sobolev spaces
论文作者
论文摘要
我们提供了足够的条件，使边界耐力不平等能够保持在有界的Lipschitz域，补充一个点（所谓的点hardy不等式），Lipschitz函数图上方的域，是偏小度lipschitz域的互补。结果，我们获得了有限的Lipschitz域中的区域分数OrliczPoincaré不平等的条件。对于有限的Lipschitz域，还给出了分数orlicz hardy和区域分数的必要条件。为分数OrliczPoincaré不平等和区域分数OrliczPoincaré不平等提供了各种足够的条件。
We provide sufficient conditions for boundary Hardy inequality to hold in bounded Lipschitz domains, complement of a point (the so-called point Hardy inequality), domain above the graph of a Lipschitz function, the complement of a bounded Lipschitz domain in fractional Orlicz-Sobolev setting. As a consequence, we get sufficient conditions for regional fractional Orlicz Poincaré inequality in bounded Lipschitz domains. Necessary conditions for fractional Orlicz Hardy and regional fractional Orlicz Poincaré inequalities are also given for bounded Lipschitz domains. Various sufficient conditions on open sets are provided for fractional Orlicz Poincaré inequality and regional fractional Orlicz Poincaré inequality to hold.
