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On the dimension of the kernel of the Dirichlet problem for fourth-order equations

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Abstract

We study the dimension of the kernel of the Dirichlet problem in the disk for fourth-order elliptic equations with constant complex coefficients in general position. Special attention is paid to improperly elliptic equations, because the kernel of the Dirichlet problem for properly elliptic equations is finite-dimensional. We single out classes of improperly elliptic equations that have properties similar to those of properly elliptic equations: the kernel of the Dirichlet problem is also finite-dimensional and in some cases even trivial. We consider fourth-order equations in general position, including equations of principal type as well as equations that have multiple characteristics and whose characteristic equation has roots ±i.

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Authors and Affiliations

  1. Donetsk National University, Vinnitsa, Ukraine

    E. A. Buryachenko

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  1. E. A. Buryachenko
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Correspondence to E. A. Buryachenko.

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Original Russian Text © E.A. Buryachenko, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 4, pp. 472–480.

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Buryachenko, E.A. On the dimension of the kernel of the Dirichlet problem for fourth-order equations. Diff Equat 51, 477–486 (2015). https://doi.org/10.1134/S0012266115040059

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