The asymptotic behaviour at infinity of solutions to the Zaremba problem for the Laplace operator in a half-cylinder is studied. Pointwise estimates for solutions, the Green function and the harmonic measure are obtained in terms of the Wiener capacity. The main result is a necessary and sufficient condition for regularity of a point at infinity.
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T.M. Kerimov, Vladimir G. Maz'ya, A.A. Novruzov, A criterion for the regularity of the infinitely distant point for the Zaremba problem in a half-cylinder (in Russian). Z. Anal. Anwend. 7 (1988), no. 2, pp. 113–125