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A formula for finding a potential from nodal lines

Authors: Joyce R. McLaughlin and Ole H. Hald
Journal: Bull. Amer. Math. Soc. 32 (1995), 241-247
MSC: Primary 35R30; Secondary 35J99, 35P20, 73D50, 73K10
MathSciNet review: 1302784
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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.

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Article copyright: © Copyright 1995 American Mathematical Society

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