标题： 关于一个非局部超导问题 显示英文标题

标题： On a nonlocal superconductivity problem

摘要： 本文研究了在超导性背景下出现的退化非局部自由边界问题，扩展了Caffarelli、Salazar和Shahgholian在局部情形下的工作\cite{CS02, CSS04}。 在这些模型中，没有偏微分方程控制梯度为零的移动集合，这意味着测试函数只需具有非零梯度。 我们的主要结果提供了粘性解的内部梯度霍尔德正则性估计。 显示英文摘要

摘要： This paper investigates degenerate nonlocal free boundary problems arising in the context of superconductivity, extending the nonlocal counterpart to the work of Caffarelli, Salazar, and Shahgholian \cite{CS02, CSS04} in the local setting. In these models, no partial differential equation governs the moving sets where the gradient vanishes, meaning that test functions are only required to have a nonzero gradient. Our main results provide interior gradient H\"older regularity estimates for viscosity solutions.