图上p-Laplace算子的特征值估计  

Eigenvalue estimates for the p-Laplace operator on the graph

作　　者：王林峰[1] Linfeng Wang

机构地区：[1]南通大学理学院,南通226019

出　　处：《中国科学：数学》2021年第8期1225-1236,共12页Scientia Sinica：Mathematica

摘　　要：设G(V,E)为满足CD_(P)^(√)(m,K)条件的连通有限图,其中p≥2,m> 0,K≤0.本文在G上考虑了方程△pu=-λ_(p)|u|^(p-2)u解的椭圆型梯度估计,其中△_(p)为p-Laplace算子.作为应用,导出了G上△_(p)的第一非零特征值的下界估计.Let G(V, E) be a connected finite graph satisfying the CD_(P)^(√)(m, K) condition for p≥2, m > 0, K≤0.In this paper we consider the elliptic gradient estimate for the solutions to the equation △pu =-λ_(p)|u|^(p-2) u on G, where △_(p) is the p-Laplace operator. As an application, we derive a lower bound estimate for the first nonzero eigenvalue of △_(p) on G.

关 键 词：连通图 P-LAPLACE算子 CD_(P)^(√)■(m K)条件 特征值估计 

分 类 号：O157.5[理学—数学]