Perturbation of zero surfaces
DOI:
https://doi.org/10.14419/gjma.v5i1.7474Keywords:
Zero Surfaces, Perturbation Theory.Abstract
It is proved that if a smooth function \(u(x), x\in R^3\), such that \(\inf_{s\in S}|u_N(s)|>0\), where \(u_N\) is the normal derivative of \(u\) on \(S\), has a closed smooth surface \(S\) of zeros, then the function \(u(x)+\epsilon v(x)\) has also a closed smooth surface \(S_\epsilon\) of zeros. Here \(v\) is a smooth function and \(\epsilon>0\) is a sufficiently small number.
References
[1] B. Fuks, Theory of analytic functions of several complex variables, AMS, Providence RI, 1963.
[2] T. Kato, Perturbation theory for linear operators, Springer Verlag, New York, 1984.
[3] A. G. Ramm, Inverse problems, Springer, New York, 2005.
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15-04-2017
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How to Cite
Ramm, A. G. (2017). Perturbation of zero surfaces. Global Journal of Mathematical Analysis, 5(1), 27-28. https://doi.org/10.14419/gjma.v5i1.7474