报告时间：2025年12月25日（周四）上午 10:00-11:00

报告地点：91国产 数学楼一楼报告厅

报告人：刘祖汉 教授，扬州大学


报告摘要：

We consider the following semilinear elliptic equation involving the fractional Laplacian

,  

where , , is the -Laplacian and is the unit ball in . We first establish an optimal H\"{o}lder regularity estimate for solutions by using blow-up analysis and Liouville-type theorems. Subsequently, we give a convergence result for sequences of solutions with uniform H\"{o}lder continuity. These results are also used to show that the Hausdorff dimension of the rupture set

satisfies:

;

.

In particular, the latter one is a new phenomenon arising from the fractional Laplacian.


邀请人：曹永罗