A NOTE ON LIOUVILLE TYPE EQUATIONS ON GRAPHS

作者：Ge, Huabin^*; Hua, Bobo; Jiang, Wenfeng

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146(11): 4837-4842.

DOI：10.1090/proc/14155

• INEQUALITIES

In this note, we study the Liouville equation Delta u = -e(u) on a graph G satisfying a certain isoperimetric inequality. Following the idea of W. Ding, we prove that there exists a uniform lower bound for the energy, Sigma(G)e(u) , of any solution u to the equation. In particular, for the 2-dimensional lattice graph Z(2) , the lower bound is given by 4.

• 出版日期2018-11
• 单位中山大学; 中国人民大学; 北京交通大学; 复旦大学