论文标题
通过抛物线抛物线差异方程式的两相Hele-shaw流动的特殊情况的规律性
Regularity for a special case of two-phase Hele-Shaw flow via parabolic integro-differential equations
论文作者
论文摘要
我们确定$ c^{1，γ} $规则性理论用于翻译不变的分数抛物线抛物线抛物线差异方程（通过Krylov-Safonov估计值）提供了针对与Hele-Shaw相关的两阶段自由度流的特殊情况的定期机制的改进。特殊情况既是由于对流的自由边界上的图形假设，又是一个假设，即空间中的自由边界为$ c^{1，\ text {dini}} $。然后，自由边界必须立即成为通用$γ$的$ c^{1，γ} $，具体取决于图形梯度的dini模量。这些结果也适用于相同类型的一相问题。
We establish that the $C^{1,γ}$ regularity theory for translation invariant fractional order parabolic integro-differential equations (via Krylov-Safonov estimates) gives an improvement of regularity mechanism for solutions to a special case of a two-phase free boundary flow related to Hele-Shaw. The special case is due to both a graph assumption on the free boundary of the flow and an assumption that the free boundary is $C^{1,\text{Dini}}$ in space. The free boundary then must immediately become $C^{1,γ}$ for a universal $γ$ depending upon the Dini modulus of the gradient of the graph. These results also apply to one-phase problems of the same type.
