We prove C1,α regularity (in the parabolic sense) for the viscosity solution of a boundary obstacle problem with a fully nonlinear parabolic equation in the interior. Following the method which was first introduced for the harmonic case by L. Caffarelli in 1979, we extend the results of I. Athanasopoulos (1982) who studied the linear parabolic case and the results of E. Milakis and L. Silvestre (2008) who treated the fully nonlinear elliptic case.

中文翻译：

---

完全非线性抛物线薄障碍问题的正则性

我们证明C1,α在内部具有完全非线性抛物方程的边界障碍问题的粘性解的规律性（在抛物线意义上）。继 L. Caffarelli 于 1979 年首次引入谐波情况的方法之后，我们扩展了研究线性抛物线情况的 I. Athanasopoulos (1982) 的结果以及 E. Milakis 和 L. Silvestre (2008) 的结果，他们研究了线性抛物线情况。处理完全非线性的椭圆情况。