A unified weighted inequality for fourth-order partial differential operators and applications

Yan Cui, Xiaoyu Fu, Jiaxin Tian

In this paper, we establish a fundamental inequality for fourth order partial differential operator $\mathcal{P}=\alpha {\partial }_s+\beta {\partial }_{ss}+{\Delta }^2$ ($\alpha ,\beta \in \mathbb{R}$) with an abstract e…