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    Harmonic Functions and Inverse Conductivity Problems on Networks

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    TR_2003-16.pdf (624.9Kb)
    No. of downloads: 677

    Date
    2003
    Author
    Berenstein, Carlos A.
    Chung, Soon-Yeong
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    Abstract
    In this paper, we discuss the inverse problem of identifying the connectivity and the conductivity of the links between adjacent pair of nodes in a network, in terms of an input-output map. To do this we introduce an elliptic operator Dw and an w-harmonic function on thegraph, with its physical interpretation been the diffusion equation on the graph, which models an electric network. After deriving the basic properties of w-harmonic functions, we prove the solvability of (direct) problems such as the Dirichlet and Neumann boundary value problems.Our main result is the global uniqueness of the inverse conductivity problem for a network under a suitable monotonicity condition.
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    http://hdl.handle.net/1903/6353
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