标题： 具有表面张力的 Stefan 问题：径向对称下物理解的独特性 显示英文标题

标题： Stefan problem with surface tension: uniqueness of physical solutions under radial symmetry

摘要： 我们研究了具有表面张力和径向对称初始数据的Stefan问题。 在这一背景下，最近在[NS23]中引入了所谓的物理解的概念，该解在全球范围内存在，尽管熔化速率固有地出现发散。 本文致力于证明物理解是唯一的，这是当自由边界不是平坦的，或者存在两相时的第一个此类结果。 主要论证依赖于对三维布朗运动的击中概率的详细分析，以及通过比较技术获得的自由边界的新型凸性性质。 在证明过程中，我们建立了大量关于自由边界和温度函数的正则性估计，这些估计本身就有意义。 显示英文摘要

摘要： We study the Stefan problem with surface tension and radially symmetric initial data. In this context, the notion of a so-called physical solution, which exists globally despite the inherent blow-ups of the melting rate, has been recently introduced in [NS23]. The paper at hand is devoted to the proof that the physical solution is unique, the first such result when the free boundary is not flat, or when two phases are present. The main argument relies on a detailed analysis of the hitting probabilities for a three-dimensional Brownian motion, as well as on a novel convexity property of the free boundary obtained by comparison techniques. In the course of the proof, we establish a wide variety of regularity estimates for the free boundary and for the temperature function, of interest in their own right.