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Improved moduli of continuity for degenerate phase transitions
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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 $p=N\geq 3$, we sharpen it to $$ \boldsymbol{\omega}(r) \approx \exp (-c| \ln r|^{\frac1N}); $$ for $p>\max\{2,N\}$, we derive an unexpected H\"older modulus.
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Logarithmic continuity for the Nonlocal degenerate two-phase Stefan problem
Weak solutions of the nonlocal p>2 two-phase Stefan problem have a logarithmic modulus of continuity up to the boundary, and a continuous weak solution of the initial-boundary value problem exists.
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