#### 【4月19日】Non-negative solutions to fractional Laplace equations with isolated singularity

2019-04-12

We study singular solutions of linear problems with fractional Laplacian.

First, we establish B\^{o}cher type theorems on a punctured ball via distributional approach.  Then, we develop a few interesting maximum principles on a punctured ball. Our distributional approach only requires the basic $L_{{\rm loc}}^1$-integrability. Furthermore, several basic lemmas are introduced to unify the treatments of Laplacian and fractional Laplacian. This is a joint work with C. Liu, Z. Wu and H. Xu.