Omega-Harmonic Functions and Inverse Conductivity Problems on Networks

Abstract

In this paper, the authors discuss the inverse problem of identifying the connectivity and conductivity of the links between adjacent pairs of nodes in a network in terms of an input-output map. To do this, they introduce an elliptic operator DELTA omega and an omega-harmonic function on the graph, with its physical interpretation being the diffusion equation on the graph, which models an electric network. After deriving the basic properties of omega-harmonic functions, they prove the solvability of (direct) problems such as the Dirichlet and Neumann boundary value problems. Their main result is the global uniqueness of the inverse conductivity problem for a network under a suitable monotonicity condition.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2003
Accession Number
ADA453137

Entities

People

  • Carlos A. Berenstein
  • Soon-yeong Chung

Organizations

  • University of Maryland

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Abstracts
  • Boundaries
  • Boundary Value Problems
  • Conductivity
  • Engineering
  • Equations
  • Governments
  • Information Operations
  • Inverse Problems
  • Maryland
  • Networks
  • Standards
  • Universities
  • Websites

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Mathematical Modeling and Probability Theory.
  • Plasma Physics / Magnetohydrodynamics