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On Dirichlet-type problems for the Lavrent’ev-Bitsadze equation

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Abstract

The existence and uniqueness issues are discussed for several boundary value problems with Dirichlet data for the Lavrent’ev-Bitsadze equation in a mixed domain. A general mixed problem (according to Bitsadze’s terminology) is considered in which the Dirichlet data are relaxed on a hyperbolic region of the boundary inside a characteristic sector with vertex on the type-change interval. In particular, conditions are pointed out under which the problem is uniquely solvable for any choice of this vertex.

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  1. Belgorod State University, ul. Pobedy 85, Belgorod, 308015, Russia

    A. P. Soldatov

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  1. A. P. Soldatov
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Original Russian Text © A.P. Soldatov, 2012, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Vol. 278, pp. 242–249.

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Soldatov, A.P. On Dirichlet-type problems for the Lavrent’ev-Bitsadze equation. Proc. Steklov Inst. Math. 278, 233–240 (2012). https://doi.org/10.1134/S0081543812060223

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  • DOI: https://doi.org/10.1134/S0081543812060223

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