论文标题
表征薄障碍物问题中紧凑的巧合集和分数laplacian的障碍物问题
Characterizing compact coincidence sets in the thin obstacle problem and the obstacle problem for the fractional Laplacian
论文作者
论文摘要
在本文中，我们将全球解决方案的全球解决方案分类为分数拉普拉斯（包括薄障碍物问题），并具有紧凑的一致性集合，并且最多在多项式增长dimension $ n \ geq 3 $中。我们以两次生物为角度在描述溶液的渐近性的一组多项式上这样做。此外，如果溶液最多具有二次增长，我们证明，紧凑的全球解决方案的巧合集也是凸。
In this paper we give a full classification of global solutions of the obstacle problem for the fractional Laplacian (including the thin obstacle problem) with compact coincidence set and at most polynomial growth in dimension $N \geq 3$. We do this in terms of a bijection onto a set of polynomials describing the asymptotics of the solution. Furthermore we prove that coincidence sets of global solutions that are compact are also convex if the solution has at most quadratic growth.
