Improved moduli of continuity for degenerate phase transitions

Abstract

We substantially improve in two scenarios the current state-of-the-art modulus of continuity for weak solutions to the $N$-dimensional, two-phase Stefan problem featuring a $p-$degenerate diffusion: for $p=N\ge 3$, we sharpen it to $$\mathbf{\omega }(r)\approx \exp (-c|\ln r{|}^{\frac{1}{N}});$$ for $p>\max \{2,N\}$, we derive an unexpected Hölder modulus.