Improved Moduli of Continuity for Degenerate Phase Transitions

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