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On the Dirichlet Problem in Rectangular Domain for Lavrentiev–Bitsadze Equation

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Abstract

We consider the Dirichlet problem in the rectangular domain for the Lavrentiev–Bitsadze equation. We find the existence conditions of the problem solution. The formulation of these conditions depend on the domain geometry, namely, on the ratio of rectangle sides from the region of hyperbolicity of the equation. Unlike other studies of similar problems, the existence conditions are obtained for the case when this ratio is a transcendental number.

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  1. Samara State Technical University, 443100, Samara, Russia

    A. A. Abashkin

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Abashkin, A.A. On the Dirichlet Problem in Rectangular Domain for Lavrentiev–Bitsadze Equation. Russ Math. 67, 1–7 (2023). https://doi.org/10.3103/S1066369X23050018

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