Free boundary regularity in nonlinear one-phase Stefan problem (2404.06712v1)

Abstract: We study the regularity of the free boundary in one-phase Stefan problem with nonlinear operator. Using the Hodograph transform and a linearization technique, we prove that flat free boundaries are $C^{1, \alpha}$ in space and time. When the operator is concave (or convex) and smooth, the free boundary is smooth.