论文标题
$ c^{2，α} $抛物线非本地障碍问题的自由边界规律性
$C^{2,α}$ regularity of free boundaries in parabolic non-local obstacle problems
论文作者
论文摘要
我们研究了抛物线障碍物问题中自由边界的规律性，用于分数laplacian $（-Δ）^s $（以及更一般的integro-differential operators）在制度$ s> \ frac {1} {2} $中的规律性。我们证明，一旦自由边界为$ c^1 $，实际上是$ c^{2，α} $。 为此，我们在$ c^1 $和$ c^{1，α} $（移动）域中建立了边界harnack不等式，提供了在边界上消失的线性方程式的两个解决方案的商与边界一样平稳。 由于我们的结果，我们还首次建立了对移动域中非局部抛物线方程的这种解决方案的最佳规律性。
We study the regularity of the free boundary in the parabolic obstacle problem for the fractional Laplacian $(-Δ)^s$ (and more general integro-differential operators) in the regime $s>\frac{1}{2}$. We prove that once the free boundary is $C^1$ it is actually $C^{2,α}$. To do so, we establish a boundary Harnack inequality in $C^1$ and $C^{1,α}$ (moving) domains, providing that the quotient of two solutions of the linear equation, that vanish on the boundary, is as smooth as the boundary. As a consequence of our results we also establish for the first time optimal regularity of such solutions to nonlocal parabolic equations in moving domains.
