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Matematicheskie Zametki, 1975, Volume 18, Issue 2, Pages 169–178 (Mi mzm7639)  

Boundary properties of functions harmonic in a strip

V. I. Gorbaichuk, P. V. Zaderej

Lutsk State Pedagogical Institute
Abstract: We study in the $L_p$-norm, $1\le p\le\infty$, the boundary properties of the solution to the Dirichlet problem for the strip
$$ \mathscr A=\{(x,y):-\infty<x<\infty,\ 0<y<\eta,\ \eta>0\} $$
and its dependence on the structural properties of the given boundary values (symmetric, antisymmetric). In particular, for the case of symmetric boundary values we obtain direct and inverse theorems on approximation in terms of the general modulus of continuity of second order.
Received: 24.01.1974
English version:
Mathematical Notes, 1975, Volume 18, Issue 2, Pages 685–691
DOI: https://doi.org/10.1007/BF01818032
Bibliographic databases:
UDC: 517.55
Language: Russian
Citation: V. I. Gorbaichuk, P. V. Zaderej, “Boundary properties of functions harmonic in a strip”, Mat. Zametki, 18:2 (1975), 169–178; Math. Notes, 18:2 (1975), 685–691
Citation in format AMSBIB
\Bibitem{GorZad75}
\by V.~I.~Gorbaichuk, P.~V.~Zaderej
\paper Boundary properties of functions harmonic in a~strip
\jour Mat. Zametki
\yr 1975
\vol 18
\issue 2
\pages 169--178
\mathnet{http://mi.mathnet.ru/mzm7639}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=419787}
\zmath{https://zbmath.org/?q=an:0312.31003}
\transl
\jour Math. Notes
\yr 1975
\vol 18
\issue 2
\pages 685--691
\crossref{https://doi.org/10.1007/BF01818032}
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