Singular Adams inequality for biharmonic operator on Heisenberg Group and its applications

The goal of this paper is to establish singular Adams type inequality for biharmonic operator on Heisenberg group. As an application, we establish the existence of a solution to \begin{equation*} \Delta_{\mathbb{H}^n}^2 u=\frac{f(\xi,u)}{\rho(\xi)^a}\,\,\text{ in }\Omega,\,\, u|_{\partial\Omega}=0=\left.\frac{\partial u}{\partial \nu}\right|_{\partial\Omega}, \end{equation*} where $0\in \Omega \subseteq \mathbb{H}^4$ is a smooth bounded domain, $0\leq a

Keywords:

• Heisenberg group
• Biharmonic equation
• Pure mathematics
• Bounded function
• Omega
• Mathematics
• Exponential function
• Mathematical analysis

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