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arXiv · 2408.11555

Improved moduli of continuity for degenerate phase transitions

Ugo Gianazza·Naian Liao·José Miguel Urbano
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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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Ugo Gianazza, Naian Liao, José Miguel Urbano. 2024-08-21. Improved moduli of continuity for degenerate phase transitions. https://arxiv.org/abs/2408.11555

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