Improved Moduli of Continuity for Degenerate Phase Transitions
Abstract
Abstract 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 $$p=N\ge 3$$ p = N ≥ 3 , we sharpen it to $$ \varvec{\omega }(r) \approx \exp (-c| \ln r|^{\frac{1}{N}}); $$ ω ( r ) ≈ exp ( - c | ln r | 1 N ) ; for $$p>\max \{2,N\}$$ p > max { 2 , N } , we derive an unexpected Hölder modulus.
Fields of Study & Subjects
Elasticity and Wave Propagation
Publication details
- Journal / source
- Annals of PDE
- Publisher
- Springer Science and Business Media LLC
- Volume
- 12
- Issue
- 2
- Pages
- 27–27
- Publication date
- 5 September 2026
- Language
- EN