论文标题
在一类非本地问题上，分数梯度约束
On a class of nonlocal problems with fractional gradient constraint
论文作者
论文摘要
我们考虑了一种希尔伯特人和一种指控方法，用于$ | d^σu| \ leq g $类型的分数梯度约束问题，涉及分布分数riesz梯度$ d^σ$，$ 0 <σ<1 $，以先前的成果呈现出这些非群体问题的解决方案和lagrange多年级的结果。 我们还证明了它们的收敛性为$σ\ nearrow1 $ to梯度约束$ | d u | \ leq g $。
We consider a Hilbertian and a charges approach to fractional gradient constraint problems of the type $|D^σu|\leq g$, involving the distributional fractional Riesz gradient $D^σ$, $0<σ<1$, extending previous results on the existence of solutions and Lagrange multipliers of these nonlocal problems. We also prove their convergence as $σ\nearrow1$ towards their local counterparts with the gradient constraint $|D u|\leq g$.
