PENDEKATAN PROBABILITAS KETAKSAMAAN HARNACK DALAM KONTEKS GRAF
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 approa...
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| Main Author: | |
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| Format: | Theses |
| Language: | Indonesia |
| Subjects: | |
| Online Access: | https://digilib.itb.ac.id/gdl/view/33872 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
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