On polytopal domains in $\mathbb{R}^3$, we prove weighted analytic regularity of solutions to the Dirichlet problem for the integral fractional Laplacian with analytic right-hand side. Employing the Caffarelli-Silvestre extension allows to localize the problem and to decompose the regularity estimates into results on vertex, edge, face, vertex-edge, vertex-face, edge-face and vertex-edge-face neighborhoods of the boundary. Using tangential differentiability of the extended solutions, a bootstrapping argument based on Caccioppoli inequalities on dyadic decompositions of the neighborhoods provides weighted, analytic control of higher order solution derivatives.

翻译：在$\mathbb{R}^3$中的多面体区域上，我们证明了具有解析右端项的分数阶拉普拉斯积分算子Dirichlet问题的加权解析正则性。利用Caffarelli-Silvestre延拓，该问题被局域化，且正则性估计可分解为边界顶点、棱边、面、顶点-棱边、顶点-面、棱边-面和顶点-棱边-面邻域上的结果。基于延拓解的切向可微性，在邻域的二进分解上利用Caccioppoli不等式通过自举论证提供了高阶解导数的加权解析控制。