Heisenberg 群上双调和算子的奇异 Adams 不等式及其应用
偏微分方程分析
2017-02-10 v2
摘要
本文的目的是建立 Heisenberg 群上双调和算子的奇异 Adams 型不等式。作为应用，我们确立了以下方程解的存在性：\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*} 其中 是光滑有界域，。该问题的特殊之处在于它包含指数非线性和奇异势。
引用
@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}
}
备注
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