Solving Boundary Value Problems on Networks Using Equilibrium Measures

@article{Bendito2000SolvingBV,
  title={Solving Boundary Value Problems on Networks Using Equilibrium Measures},
  author={Enrique Bendito and {\'A}ngeles Carmona and Andr{\'e}s M. Encinas},
  journal={Journal of Functional Analysis},
  year={2000},
  volume={171},
  pages={155-176}
}
Abstract The purpose of this paper is to construct solutions of self-adjoint boundary value problems on finite networks. To this end, we obtain explicit expressions of the Green functions for all different boundary value problems. The method consists of reducing each boundary value problem either to a Dirichlet problem or to a Poisson equation on a new network closely related with the former boundary value problem. In this process we also get an explicit expression of the Poisson kernel for the… 

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