For the obstacle problem involving a convex fully nonlinear elliptic operator, we show that the singular set in the free boundary stratifies. The top stratum is locally covered by a $C^{1,\alpha}$-manifold, and the lower strata are covered by $C^{1,\log^\varepsilon}$-manifolds. This essentially recovers the regularity result obtained by Figalli-Serra when the operator is the Laplacian.

中文翻译：

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完全非线性障碍问题中奇异集的正则性

对于涉及凸完全非线性椭圆算子的障碍问题，我们证明了自由边界中的奇异集分层。上层局部被$C^{1,\alpha}$-流形覆盖，下层被$C^{1,\log^\varepsilon}$-流形覆盖。这基本上恢复了当算子是拉普拉斯算子时 Figalli-Serra 得到的规律性结果。