Session S38 - Geometric Potential Analysis

Friday, July 16, 20:10 ~ 20:40 UTC-3

The fractional Laplacian and fractional gradient operators

Liguang Liu

Renmin University of China, China   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We will talk about some recent results related to the fractional Laplacian $\nabla^s_+=(-\Delta)^{\frac s2} $ and the fractional gradient $\nabla^s_-=\nabla (-\Delta)^{\frac {s-1}{2}}$, including also some optimal inequalities of type Hardy-Rellich/Adams-Moser/Morrey-Sobolev, and regularity of the distributional solutions to the dual equations $[\nabla^s_\pm]^\ast u=f$.

Joint work with Jie Xiao (Memorial University, Canada).

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