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On boundary-value problems for a second-order differential equation with complex coefficients in a plane domain

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Abstract

We study boundary-value problems for a homogeneous partial differential equation of the second order with arbitrary constant complex coefficients and a homogeneous symbol in a bounded domain with smooth boundary. Necessary and sufficient conditions for the solvability of the Cauchy problem are obtained. These conditions are written in the form of a moment problem on the boundary of the domain and applied to the investigation of boundary-value problems. This moment problem is solved in the case of a disk.

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Authors
  1. V. P. Burskii
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Burskii, V.P. On boundary-value problems for a second-order differential equation with complex coefficients in a plane domain. Ukr Math J 48, 1647–1658 (1996). https://doi.org/10.1007/BF02529486

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  • DOI: https://doi.org/10.1007/BF02529486

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