论文标题
二阶Sobolev不平等的极端功能在多项式生长组上
Extremal functions for the second-order Sobolev inequality on groups of polynomial growth
论文作者
论文摘要
在本文中，我们证明了多项式生长群的Cayley图上的二阶Sobolev不等式。我们使用离散的浓度 - 触觉原理来证明在超临界情况下最佳常数的极端函数。作为应用程序，我们获得了$ p $ biharmonic方程和车道填充系统的积极基础解决方案。
In this paper, we prove the second-order Sobolev inequalities on Cayley graphs of groups of polynomial growth. We use the discrete Concentration-Compactness principle to prove the existence of extremal functions for best constants in supercritical cases. As applications, we get the existence of positive ground state solutions to the $p$-biharmonic equations and the Lane-Emden systems.
