源于两相Stefan问题的一个传输问题
A transmission problem arising from the two-phase Stefan problem
AI总结：
本文研究源于两相非齐次Stefan问题线性化极限的抛物型传输问题，证明了经典解的存在唯一性、广义传输问题的Harnack不等式及界面附近的$C^{1,α}$估计，可用于推导带分布源的两相Stefan问题平坦自由边界的正则性。
AI中文摘要：
我们研究一类界面条件依赖解的时间导数的抛物型传输问题。该模型是经速端变换后，两相非齐次Stefan问题线性化极限形态的自然产物。我们的主要结果证明了经典解的存在性与唯一性。我们还证明了一类广义传输问题的Harnack不等式，并建立了从界面两侧直至界面的$C^{1,α}$估计。这些结果可用于获得带分布源的两相Stefan问题平坦自由边界的$C^{1,α}$正则性。
英文摘要：
We study a parabolic transmission problem whose interface condition depends on the time derivative of the solution. This model arises naturally as the linearized limiting profile of a two-phase inhomogeneous Stefan problem after the hodograph transform. Our main result shows the existence and uniqueness of a classical solution. We also prove a Harnack inequality for a general class of transmission problems and establish $C^{1,α}$ estimates up to the interface from both sides. These results can be used to obtain $C^{1,α}$ regularity of flat free boundaries for the two-phase Stefan problem with distributed sources.
