A formula for finding a potential from nodal lines
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 by Joyce R. McLaughlin and Ole H. Hald PDF
 Bull. Amer. Math. Soc. 32 (1995), 241247 Request permission
Abstract:
In this announcement we consider an eigenvalue problem which arises in the study of rectangular membranes. The mathematical model is an elliptic equation, in potential form, with Dirichlet boundary conditions. We have shown that the potential is uniquely determined, up to an additive constant, by a subset of the nodal lines of the eigenfunctions. A formula is given which, when the additive constant is fixed, yields an approximation to the potential at a dense set of points. An estimate is presented for the error made by the formula.References

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Additional Information
 © Copyright 1995 American Mathematical Society
 Journal: Bull. Amer. Math. Soc. 32 (1995), 241247
 MSC: Primary 35R30; Secondary 35J99, 35P20, 73D50, 73K10
 DOI: https://doi.org/10.1090/S027309791995005847
 MathSciNet review: 1302784