论文标题
分数椭圆形问题的对称：一种直接方法
Symmetrization for fractional elliptic problems: a direct approach
论文作者
论文摘要
我们提供了新的直接方法来建立对称化的结果，以质量浓度（即积分）比较的形式，用于$（ - δ）^{s} U = f $ $（0 <s <s <s <1）$的分数椭圆方程，配备有均匀的边界条件。经典的Pointwenteri重新排列不平等的不平等现象以$ s \ rightarrow1 $恢复。最后，为所有$ s \ in（0,1）$中构建的明确反例强调，同一估计值不能在非局部设置中保持，从而显示了我们结果的最佳性。
We provide new direct methods to establish symmetrization results in the form of mass concentration (i.e., integral) comparison for fractional elliptic equations of the type $(-Δ)^{s}u=f$ $(0<s<1)$ in a bounded domain $Ω$, equipped with homogeneous boundary conditions. The classical pointwise Talenti rearrangement inequality is recovered in the limit $s\rightarrow1$. Finally, explicit counterexamples constructed for all $s\in(0,1)$ highlight that the same pointwise estimate cannot hold in a nonlocal setting, thus showing the optimality of our results.
