论文标题
自由边界较薄的矢量问题
A vectorial problem with thin free boundary
论文作者
论文摘要
我们将\ cite {crs}引入的薄边界问题的矢量类似物视为实现经典伯努利问题的非本地版本的实现。我们研究局部最小化器的最佳规律性，非高度和密度特性。通过基于魏斯型单调性公式的爆破分析，我们表明自由边界是“常规”和“单数”部分的结合。最后，我们使用一种粘度方法来证明自由边界的常规部分的$ c^{1，α} $。
We consider the vectorial analogue of the thin free boundary problem introduced in \cite{CRS} as a realization of a nonlocal version of the classical Bernoulli problem. We study optimal regularity, nondegeneracy, and density properties of local minimizers. Via a blow-up analysis based on a Weiss type monotonicity formula, we show that the free boundary is the union of a "regular" and a "singular" part. Finally we use a viscosity approach to prove $C^{1,α}$ regularity of the regular part of the free boundary.
