论文标题
$ h^{1+α} $估计完全非线性抛物线薄障碍物问题
$H^{1+α}$ estimates for the fully nonlinear parabolic thin obstacle problem
论文作者
论文摘要
我们研究了粘度解决方案的规律性解决完全非线性的抛物线薄障碍物问题。特别是，我们证明该解决方案是光滑障碍物的每一侧的本地$ h^{1+α} $，对于一些小$α> 0。我们的结果还通过两种方式扩展了Chatzigeorgiou（2019）的结果。首先，我们不认为解决方案和操作员是对称的。其次，我们的估计是本地的，从某种意义上说，不依赖边界数据。
We study the regularity of the viscosity solution to the fully nonlinear parabolic thin obstacle problem. In particular, we prove that the solution is local $H^{1+α}$ on each side of the smooth obstacle, for some small $α>0.$ Following the method which was first introduced for the harmonic case by Caffarelli in 1979, we extend the results of Fernández-Real (2016) who treated the fully nonlinear elliptic case. Our results also extend those of Chatzigeorgiou (2019) in two ways. First, we do not assume solutions nor operators to be symmetric. Second, our estimates are local, in the sense that do not rely on the boundary data.
