In terms of weak solutions of the fractional p‐Laplace equation with measure data, this paper offers a dual characterization for the fractional Sobolev capacity on bounded domain. In addition, two further results are given: one is an equivalent estimate for the fractional Sobolev capacity; the other is the removability of sets of zero capacity and its relation to solutions of the fractional p‐Laplace equation.

中文翻译：

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通过分数p-Laplace方程的解对分数容量进行双重表征

关于分数p-拉普拉斯方程具有测度数据的弱解，本文对有界域上的分数Sobolev容量提供了双重表征。另外，给出了另外两个结果：一个是分数Sobolev容量的等效估计值；另一个是对Sobolev容量分数的等效估计。另一个是零容量集的可移动性及其与分数p -Laplace方程解的关系。