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Zeitschrift für Analysis und ihre Anwendungen


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Volume 7, Issue 2, 1988, pp. 113–125
DOI: 10.4171/ZAA/288

Published online: 1988-04-30

A criterion for the regularity of the infinitely distant point for the Zaremba problem in a half-cylinder (in Russian)

T.M. Kerimov, Vladimir G. Maz'ya[1] and A.A. Novruzov

(1) Linköping University, Sweden

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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Kerimov T.M., Maz'ya Vladimir, Novruzov A.A.: 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), 113-125. doi: 10.4171/ZAA/288