论文标题
强大的非局部痕量空间和诺伊曼问题
Robust nonlocal trace spaces and Neumann problems
论文作者
论文摘要
我们证明了（0,1）$的订单$ s \ sobolev空间的痕迹和扩展结果。这些空间用于对有限域的非局部迪里奇和诺伊曼问题的研究。由于$ s $接近$ 1 $，因此结果是稳健的，因为痕迹和扩展运算符的连续性是均匀的，并且我们的痕迹空间会收敛到$ h^{1/2}（\ partialω）$。我们应用这些结果来研究非局部诺伊曼问题的解决方案的收敛性，因为内部差异算子以差异形式定位于对称的二阶操作员。
We prove trace and extension results for fractional Sobolev spaces of order $s\in(0,1)$. These spaces are used in the study of nonlocal Dirichlet and Neumann problems on bounded domains. The results are robust in the sense that the continuity of the trace and extension operators is uniform as $s$ approaches $1$ and our trace spaces converge to $H^{1/2}(\partial Ω)$. We apply these results in order to study the convergence of solutions of nonlocal Neumann problems as the integro-differential operators localize to a symmetric, second order operator in divergence form.
