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Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian
Mathematical Models and Methods in Applied Sciences ( IF 3.6 ) Pub Date : 2019-10-18 , DOI: 10.1142/s021820251950057x
Juan Pablo Borthagaray 1 , Ricardo H. Nochetto 2 , Abner J. Salgado 3
Affiliation  

We obtain regularity results in weighted Sobolev spaces for the solution of the obstacle problem for the integral fractional Laplacian [Formula: see text] in a Lipschitz bounded domain [Formula: see text] satisfying the exterior ball condition. The weight is a power of the distance to the boundary [Formula: see text] of [Formula: see text] that accounts for the singular boundary behavior of the solution for any [Formula: see text]. These bounds then serve us as a guide in the design and analysis of a finite element scheme over graded meshes for any dimension [Formula: see text], which is optimal for [Formula: see text].

中文翻译:

积分分数拉普拉斯算子障碍问题的加权 Sobolev 正则性和逼近率

我们在加权 Sobolev 空间中获得规律性结果,用于解决在 Lipschitz 有界域 [公式:见文本] 中满足外球条件的积分分数拉普拉斯算子 [公式:见文本] 的障碍问题。权重是 [公式:参见文本] 到边界 [公式:参见文本] 的距离的幂,它解释了任何 [公式:参见文本] 的解的奇异边界行为。然后,这些界限可以作为我们设计和分析任何维度的分级网格上的有限元方案的指南 [公式:参见文本],这对于 [公式:参见文本] 是最佳的。
更新日期:2019-10-18
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