Bitsadze-Samarskii problem with a lacking shift condition for the Gellerstedt equation with a singular coefficient

For the Gellerstedt equation with a singular coefficient, we study the well-posedness of the problem with the Bitsadze-Samarskii conditions on the ellipticity boundary and on a segment of the degeneration line and with a shift condition on parts of boundary characteristics. We use the maximum principle to prove the uniqueness of the solution of the problem in the class of Hölder functions and the method of integral equations to prove its existence.

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