Singular Adams inequality for biharmonic operator on Heisenberg Group and its applications
Abstract
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 is a smooth bounded domain, The special feature of this problem is that it contains an exponential nonlinearity and singular potential.
Keywords
Cite
@article{arxiv.1606.06414,
title = {Singular Adams inequality for biharmonic operator on Heisenberg Group and its applications},
author = {Gaurav Dwivedi and Jagmohan Tyagi},
journal= {arXiv preprint arXiv:1606.06414},
year = {2017}
}
Comments
There is small correction in this version. For our results to be meaningful, we need to work with the case Q=4 instead of Q=10. So throughout the article, We have now taken Q=4, that is we are working with one dimensional Heisenberg group. All the proofs remain unaffected due to this change