The Dirichlet problem and the construction of superharmonic functions with point harmonic singularities are two of the basic problems in potential theory. In this article, we study these problems in the context of discrete potential theory, which leads to the consideration of Green’s formulas and flux on a Cartier tree.
"Dirichlet problem and Green's formulas on trees." Hiroshima Math. J. 35 (3) 413 - 424, November 2005. https://doi.org/10.32917/hmj/1150998320