论文标题
罗宾问题在非平滑域中的边界行为
Boundary behavior of Robin problems in non-smooth domains
论文作者
论文摘要
我们分析了在边界上的严格阳性，用于一般（非平滑）域的罗宾问题的非负溶液，例如具有有限的Hausdorff度量的可矫正拓扑边界的开放式设置。这个问题是在2008年由低音，Burdzy和Chen在概率背景下提出的。我们提供几何条件，使得与$ p $ laplacian类型的通用椭圆运算符相关的罗宾问题的解决方案，右手侧为正，在边界处远离零的全球或本地界限。我们的变分类型方法依赖于集合的等值谱的分析，并提供了定量估计。
We analyze strict positivity at the boundary for nonnegative solutions of Robin problems in general (non-smooth) domains, e.g. open sets with rectifiable topological boundaries having finite Hausdorff measure. This question was raised by Bass, Burdzy and Chen in 2008 for harmonic functions, in a probabilistic context. We give geometric conditions such that the solutions of Robin problems associated to general elliptic operators of $p$-Laplacian type, with a positive right hand side, are globally or locally bounded away from zero at the boundary. Our method, of variational type, relies on the analysis of an isoperimetric profile of the set and provides quantitative estimates as well.
