论文标题
分数sobolev-poincaré和（本地化的）耐力不平等的表征
Characterization of fractional Sobolev--Poincaré and (localized) Hardy inequalities
论文作者
论文摘要
在本文中，我们证明了分数Sobolev-Poincaré的不平等现象的电容性版本。我们通过$ \ mathbb {r}^n $中域的均匀脂肪条件来表征边界分数sobolev-poincaré的局部变体。分数Hardy不平等的存在类型结果是在超临界的情况下建立的$ sp> n $，in（0,1）$，$ p> 1 $。还解决了通过关联问题的较弱的较弱的较弱的不平等表征。
In this paper, we prove capacitary versions of the fractional Sobolev--Poincaré inequalities. We characterize localized variant of the boundary fractional Sobolev--Poincaré inequalities through uniform fatness condition of the domain in $\mathbb{R}^n$. Existence type results on the fractional Hardy inequality are established in the supercritical case $sp>n$ for $s\in(0,1)$, $p>1$. Characterization of the fractional Hardy inequality through weak supersolution of the associate problem is also addressed.
