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Differential operators defining a solution of an elliptic-type equation

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Abstract

We construct differential operators Kg(z), Lg(z), \(Kg(z),\;Lg(z),\,\,M\overline {f(z)} ,\), and \(N\overline {f(z)} \) such that they map arbitrary holomorphic functions in a simply connected domain D in the complex plane z=x+iy into regular solutions of the equation

$$W_{ \approx \bar \approx } + A(z,\bar z)W_{\bar \approx } + B(z,z)W = 0.$$

We give examples of applications of the constructed differential operators to a solution of the main boundary-value problems of mathematical physics. Bibliography: 1 title.

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References

  1. I. N. Aleksandrovich, “Differential operators defining a solution of a certain class of elliptic type equations,”Ukr. Mat. Zh.,41, No. 6, 825–828 (1989).

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Authors
  1. I. M. Aleksandrovich
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  2. M. V. Sidorov
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Additional information

Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 81, 19997, pp. 1–8.

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Aleksandrovich, I.M., Sidorov, M.V. Differential operators defining a solution of an elliptic-type equation. J Math Sci 102, 3719–3726 (2000). https://doi.org/10.1007/BF02680223

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  • DOI: https://doi.org/10.1007/BF02680223

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