论文标题
缓慢消失的平均振荡：在两相的自由边界问题中爆炸的非唯一性
Slowly vanishing mean oscillations: non-uniqueness of blow-ups in a two-phase free boundary problem
论文作者
论文摘要
在Kenig和Toro的两阶段无边界问题中，人们研究了辅助NTA结构域的谐波测量的radon-nikodym衍生物$ h =dΩ^ - /dω^+$的规律性如何控制其共同边界的几何形状。现在知道，$ \ log h \ in c^{0，α}（\partialΩ）$表示，边界有唯一的爆炸，这是同质谐波多项式的零集。在本说明中，我们给出了$ \ log h \ c（\ partialω）$的域示例，其边界的点具有非唯一的爆炸点。从哲学上讲，这些例子是由无限量的振荡或旋转爆炸限制而产生的，但非常缓慢。
In Kenig and Toro's two-phase free boundary problem, one studies how the regularity of the Radon-Nikodym derivative $h= dω^-/dω^+$ of harmonic measures on complementary NTA domains controls the geometry of their common boundary. It is now known that $\log h \in C^{0,α}(\partial Ω)$ implies that pointwise the boundary has a unique blow-up, which is the zero set of a homogeneous harmonic polynomial. In this note, we give examples of domains with $\log h \in C(\partial Ω)$ whose boundaries have points with non-unique blow-ups. Philosophically the examples arise from oscillating or rotating a blow-up limit by an infinite amount, but very slowly.
