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Solvability of boundary value problems for second-order elliptic differential-operator equations with a spectral parameter and with a discontinuous coefficient at the highest derivative

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Abstract

In a Hilbert space H, we study the solvability of boundary value problems for second-order elliptic differential-operator equations with a spectral parameter and with a discontinuous (piecewise constant) coefficient at the highest derivative. At the point of discontinuity, we find a transmission condition, which contains a linear unbounded operator. We present an application of the results to elliptic boundary value problems.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, National Academy of Sciences, Baku, Azerbaijan Tel-Aviv University, Tel-Aviv, Israel

    B. A. Aliev & Ya. Yakubov

Authors
  1. B. A. Aliev
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  2. Ya. Yakubov
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Correspondence to B. A. Aliev.

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Original Russian Text © B.A. Aliev, Ya. Yakubov, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 4, pp. 468–479.

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Aliev, B.A., Yakubov, Y. Solvability of boundary value problems for second-order elliptic differential-operator equations with a spectral parameter and with a discontinuous coefficient at the highest derivative. Diff Equat 50, 464–475 (2014). https://doi.org/10.1134/S0012266114040053

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  • DOI: https://doi.org/10.1134/S0012266114040053

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