What question did this study set out to answer?

Determine whether a near-constant internal conductivity distribution in a two-dimensional body can be uniquely reconstructed using only steady-state boundary current measurements.

January 1, 1986Communications on Pure and Applied Mathematics

A uniqueness theorem for an inverse boundary value problem in electrical prospection

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Authors

JSJohn SylvesterUniversity of Wisconsin–Madison GUGünther UhlmannUniversity of Minnesota

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Implication

Theoretical analysis demonstrates unique recovery of near-constant conductivity in two-dimensional bodies, suggesting electrical boundary measurements reliably identify internal structures.

Key Points

Determine whether a near-constant internal conductivity distribution in a two-dimensional body can be uniquely reconstructed using only steady-state boundary current measurements.
Formulated an inverse boundary value problem modeling electrical prospection across a two-dimensional domain.
Evaluated the divergence-form differential operator ∇·γ∇ through Dirichlet integrals corresponding to steady-state boundary voltage and current measurements.
Demonstrated that a near-constant conductivity field in a two-dimensional medium is uniquely determined by boundary direct current data.
Proved that the unknown coefficient γ within the operator ∇·γ∇ is uniquely specified by its corresponding Dirichlet integrals.

Cite This Study

Sylvester et al. (1986) studied this question.

synapsesocial.com/papers/6a72dce7b8533585dd0873fe https://doi.org/10.1002/cpa.3160390106

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Implication

Theoretical analysis demonstrates unique recovery of near-constant conductivity in two-dimensional bodies, suggesting electrical boundary measurements reliably identify internal structures.

A uniqueness theorem for an inverse boundary value problem in electrical prospection

Discussion

Member takes

Implication

Key Points

Cite This Study

A uniqueness theorem for an inverse boundary value problem in electrical prospection

Discussion

Member takes

Implication

Key Points

Cite This Study

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