论文标题
无限元图上的离散谐波功能
Discrete harmonic functions on infinite penny graphs
论文作者
论文摘要
在本文中，我们研究了无限一分钱图上的离散谐波函数。对于具有有界面部程度的无限一分钱图，我们证明了体积的属性和庞加莱不平等的倍增性，这产生了harnack不平等的正常谐波功能。此外，我们证明了具有有限生长速率的多项式生长谐波函数的空间或热方程的古代解决方案具有有限的尺寸特性。
In this paper, we study discrete harmonic functions on infinite penny graphs. For an infinite penny graph with bounded facial degree, we prove that the volume doubling property and the Poincaré inequality hold, which yields the Harnack inequality for positive harmonic functions. Moreover, we prove that the space of polynomial growth harmonic functions, or ancient solutions of the heat equation, with bounded growth rate has finite dimensional property.
