Elliptic boundary value problems with periodic coefficients in a cylinder

In a domain with periodically varying cross-section, this paper studies boundary value problems, elliptic in the Douglis–Nirenberg sense, in which the coefficients are periodic functions with the same period. Necessary and sufficient conditions for the unique solvability of these problems in function spaces with weighted norms are proved, and theorems on the Noether property and on the asymptotics of the solutions of boundary value problems with exponentially small perturbations of the coefficients are adduced.
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