ON AN ANISOTROPIC BOUNDARY PROBLEM OF DIFFRACTION WITH FIRST AND SECOND TYPE BOUNDARY CONDITIONS

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Submitted: 2025-02-23; Published: 2025-02-23

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Abstract

In the present paper solvability of a class of boundary problems associated with the anisotropic Helmholtz–Shrodinger equation in the upper and lower semiplanes of Sobolev spaces is studied. The first and second type boundary conditions are assumed to hold on the line y=0. Solvability of these boundary problems reduces to solvability of Riman–Hilbert boundary problem. The solvability analysis is based on the factorization problem of some matrix-function.