论文标题
外部和环形组中分数过度确定问题的定量结果
Quantitative results for fractional overdetermined problems in exterior and annular sets
论文作者
论文摘要
我们考虑与分数能力有关的过度确定问题。特别是我们研究了在无界外部集合或有限环形组中定义的$ s $ harmonic函数，并具有平行于边界的级别集。我们首先通过证明域和解决方案本身是径向对称的，首先对过度确定问题的解决方案进行了分类。然后，我们证明了对称结果的定量稳定性对应物：我们假设过度确定的条件略有干扰，并且我们以定量的方式测量了该域接近对称集的多少。
We consider overdetermined problems related to the fractional capacity. In particular we study $s$-harmonic functions defined in unbounded exterior sets or in bounded annular sets, and having a level set parallel to the boundary. We first classify the solutions of the overdetermined problems, by proving that the domain and the solution itself are radially symmetric. Then we prove a quantitative stability counterpart of the symmetry results: we assume that the overdetermined condition is slightly perturbed and we measure, in a quantitative way, how much the domain is close to a symmetric set.
