论文标题
艾伦（Allen）的欧几里得等级问题中的均匀稳定性 - -CAHN能量
Uniform stability in the Euclidean isoperimetric problem for the Allen--Cahn energy
论文作者
论文摘要
我们考虑了Allen-cahn Energy功能上整个$ \ Mathbb {r}^n $定义的等等问题。对于非脱位双井电位，我们证明了二次类型的急剧定量稳定性不平等，它们在相变的长度尺度上是均匀的。我们还得出了类似于恒定平均曲率边界的经典Alexandrov定理的临界点的刚度定理。
We consider the isoperimetric problem defined on the whole $\mathbb{R}^n$ by the Allen--Cahn energy functional. For non-degenerate double well potentials, we prove sharp quantitative stability inequalities of quadratic type which are uniform in the length scale of the phase transitions. We also derive a rigidity theorem for critical points analogous to the classical Alexandrov's theorem for constant mean curvature boundaries.
