A formula for finding a potential from nodal lines

McLaughlin, Joyce R.; Hald, Ole H.

doi:10.1090/S0273-0979-1995-00584-7

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), 241-247 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.

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Stabile Eigenwerte des Laplace-Operators auf Speziellen Tori