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The singular set in the Stefan problem

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 نشر من قبل Xavier Ros-Oton
 تاريخ النشر 2021
  مجال البحث
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In this paper we analyze the singular set in the Stefan problem and prove the following results: - The singular set has parabolic Hausdorff dimension at most $n-1$. - The solution admits a $C^infty$-expansion at all singular points, up to a set of parabolic Hausdorff dimension at most $n-2$. - In $mathbb R^3$, the free boundary is smooth for almost every time $t$, and the set of singular times $mathcal Ssubset mathbb R$ has Hausdorff dimension at most $1/2$. These results provide us with a refined understanding of the Stefan problems singularities and answer some long-standing open questions in the field.

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