Nondegeneracy for stable solutions to the one-phase free boundary problem
Nondegeneracy for stable solutions to the one-phase free boundary problem
复制标题
一相自由边界问题稳定解的非简并性
DOI：
10.1007/s00208-023-02591-0
复制
发表时间：
2022
影响因子：
1.4
通讯作者：
Kelei Wang
中科院分区：
文献类型：
--
作者：
Nikola Kamburov;Kelei Wang
证明了单相自由边界问题稳定解的非退化条件。证明是通过De Giorgi迭代，其中我们需要Michael和Simon的Soblev不等式，从而需要自由边界平均曲率的积分估计。然后，我们应用非退化估计得到n维稳定自由边界的局部曲率界，只要同一维稳定整体解的Bernstein型定理是有效的。特别地，我们得到了$$n=2$$n=2维的曲率估计。
We prove the nondegeneracy condition for stable solutions to the one-phase free boundary problem. The proof is by a De Giorgi iteration, where we need the Sobolev inequality of Michael and Simon and, consequently, an integral estimate for the mean curvature of the free boundary. We then apply the nondegeneracy estimate to obtain local curvature bounds for stable free boundaries in dimension n , provided the Bernstein-type theorem for stable, entire solutions in the same dimension is valid. In particular, we obtain this curvature estimate in $$n=2$$ n = 2 dimensions.
几乎最小化的自由边界正则性
影响因子：
1.7
作者：
David, Guy;Engelstein, Max;Toro, Tatiana
通讯作者：
Toro, Tatiana