分数Hardy常数的Galerkin逼近
Galerkin Approximation of the Fractional Hardy Constant
AI总结：
该研究针对N≥1维、特定分数指数的分数Hardy不等式，采用分段线性元的Galerkin逼近方法，在含原点的有界凸光滑域上，建立了其离散最优常数的精确估计及对应收敛率。
AI中文摘要：
我们针对N≥1维、分数指数s∈(0,min{1,N/2})的分数Hardy不等式的离散最优常数建立了精确估计；当在包含原点的有界凸光滑域中采用拟一致正则网格、用分段线性元进行Galerkin逼近计算时，我们确定的收敛率成立。
英文摘要：
We establish sharp estimates for the discrete optimal constant of the fractional Hardy Inequality in dimension $N\geq 1$, with fractional exponent $s\in \left(0,\min\left\{1,\frac{N}{2}\right\}\right)$. The convergence rates that we establish take place for the Galerkin approximation with piecewise linear elements, when the computations are carried out in a bounded, convex and smooth domain containing the origin, for which we employ a quasi-uniform and regular mesh.
