We prove weighted analytic regularity of solutions to the Dirichlet problem for the integral fractional Laplacian in polytopal three-dimensional domains and 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 control of higher order derivatives.

翻译：我们证明了在多面体三维区域中，具有解析右端项的积分分数阶拉普拉斯算子狄利克雷问题解的加权解析正则性。利用Caffarelli-Silvestre延拓方法，可将问题局部化，并将正则性估计分解为边界处顶点、边、面、顶点-边、顶点-面、边-面以及顶点-边-面邻域上的结果。基于延拓解的切向可微性，通过在这些邻域的二进分解上应用Caccioppoli不等式进行自举论证，从而实现对高阶导数的控制。