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Differential operators determining solutions of Elliptic equations

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Ukrainian Mathematical Journal Aims and scope

Abstract

We construct differential operatorsLg(z), Kg(z), Nf¯(z), Mf¯z) which map arbitrary functions holomorphic in a simply connected domainD of the planez=x+iy into regular solutions of the equation

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

and present examples of the application of these differential operators to the solution of fundamental boundary-value problems in mathematical physics.

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Reference

  1. E. N. Aleksandrovich, “Differential operators determining solutions of one class of elliptic equations,”Ukr. Mat. Zh.,41, No. 6, 825–828 (1989).

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Authors and Affiliations

  1. Kiev University, Kiev

    I. M. Aleksandrovich

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  1. I. M. Aleksandrovich
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 12, pp. 1587–1592, December, 1995.

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Aleksandrovich, I.M. Differential operators determining solutions of Elliptic equations. Ukr Math J 47, 1811–1817 (1995). https://doi.org/10.1007/BF01060956

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  • DOI: https://doi.org/10.1007/BF01060956

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