A Formula for Finding a Potential from Nodal Lines
Analysis of PDEs
2016-09-06 v1
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.
Cite
@article{arxiv.math/9504226,
title = {A Formula for Finding a Potential from Nodal Lines},
author = {Joyce R. McLaughlin and Ole H. Hald},
journal= {arXiv preprint arXiv:math/9504226},
year = {2016}
}
Comments
7 pages