论文标题
2D薄障碍物问题无穷大的数据
2D Thin obstacle problem with data at infinity
论文作者
论文摘要
在本文中，我们考虑了$ \ mathbb {r}^2 $中的薄障碍物问题，该数据具有无限的数据。我们首先证明了它的存在和独特性。然后，我们证明其对称解决方案实际上是半空间解决方案。当对半空间$（2k- \ frac {1} {2}）$ - 均质的解决方案分类为$ \ mathbb {r}^3 $中的薄障碍物问题时，我们的结果是需要的。这是对Savin-yu工作的一部分的概括\ cite {savin2021halfspace}对半空间$ \ frac {7} {2} $ - 同质解决方案进行分类。
In this paper, we consider the thin obstacle problem in $\mathbb{R}^2$ with data at infinity. We first prove the existence and uniqueness of it. Then we show that its symmetric solutions are actually half-space solutions. Our results are needed when classifying the half-space $(2k-\frac{1}{2})$-homogeneous solutions to the thin obstacle problems in $\mathbb{R}^3$. It is a generalization of one part of Savin-Yu's work \cite{savin2021halfspace} on classifying the half-space $\frac{7}{2}$-homogeneous solutions.
