PENDEKATAN PROBABILITAS KETAKSAMAAN HARNACK DALAM KONTEKS GRAF - Rika Ayu Febrilia, Baiq
In this study we introduce a probabilistic approach to prove the following Harnack inequality in the context of graphs, max B u C min B u; where B is a ball in the context of graph, C is a constant and u is a solution Lu(x) = 0 where Lu(x) := X yx p(x; y) (u(x) ???? u(y)) : This approach is based on a critical density property and doubling property. With this new approach, Harnack inequality can be obtained without using John-Nirenberg inequality and covering lemmas.