Perturbation of zero surfaces

  • Abstract
  • Keywords
  • References
  • PDF
  • 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.

  • Keywords

    Zero Surfaces; Perturbation Theory.

  • 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.




Article ID: 7474
DOI: 10.14419/gjma.v5i1.7474

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