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Basis property of eigenfunctions of the Frankl problem with a nonlocal evenness condition and with a discontinuity in the solution gradient

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Abstract

In the present paper, we write out the eigenfunctions of the Frankl problem with a nonlocal evenness condition and with a discontinuity of the normal derivative of the solution on the line of change of type of the equation. We show that these eigenfunctions form a Riesz basis in the elliptic part of the domain. In addition, we prove the Riesz basis property on [0, π/2] of the system of cosines occurring in the expressions for the eigenfunctions. Earlier, the Riesz basis property was proved for the eigenfunctions of the Frankl problem with a nonlocal evenness condition and with continuous solution gradient.

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References

  1. Zygmund, A., Trigonometric Series, Cambridge: At the University Press, 1959. Translated under the title Trigonometricheskie ryady, Moscow: Mir, 1965, vol. 1.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    E. I. Moiseev & N. Abbasi

  2. Computer Center, Russian Academy of Sciences, Moscow, Russia

    E. I. Moiseev & N. Abbasi

  3. University of Lorestan, Lorestan, Islamic Republic of Iran

    E. I. Moiseev & N. Abbasi

Authors
  1. E. I. Moiseev
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  2. N. Abbasi
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Additional information

Original Russian Text © E.I. Moiseev, N. Abbasi, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 10, pp. 1399–1404.

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Moiseev, E.I., Abbasi, N. Basis property of eigenfunctions of the Frankl problem with a nonlocal evenness condition and with a discontinuity in the solution gradient. Diff Equat 44, 1460–1466 (2008). https://doi.org/10.1134/S0012266108100121

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  • DOI: https://doi.org/10.1134/S0012266108100121

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