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Zapiski Nauchnykh Seminarov POMI, 2000, Volume 270, Pages 51–79 (Mi znsl1327)  
This article is cited in 7 scientific papers (total in 7 papers)

Mixed Stekloff eigenvalue problem and new extremal properties of the Grötzsch ring

B. Dittmara, A. Yu. Solyninb

a Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (318 kB) Citations (7)
Abstract: We study the mixed Stekloff eigenvalue problem in doubly-connected domains. Using circular symmetrization and a distortion theorem on conformal mapping of an annulus, we find a lower bound for the first eigenvalue that is sharp for the Grötzsch ring. We solve also an extremal problem for some polygonal doubly-connected domains and prove some results concerning the existence of a closed nodal line.
Received: 03.04.2000
English version:
Journal of Mathematical Sciences (New York), 2003, Volume 115, Issue 2, Pages 2119–2134
DOI: https://doi.org/10.1023/A:1022876518846
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: B. Dittmar, A. Yu. Solynin, “Mixed Stekloff eigenvalue problem and new extremal properties of the Grötzsch ring”, Investigations on linear operators and function theory. Part 28, Zap. Nauchn. Sem. POMI, 270, POMI, St. Petersburg, 2000, 51–79; J. Math. Sci. (N. Y.), 115:2 (2003), 2119–2134
Citation in format AMSBIB
\Bibitem{DitSol00}
\by B.~Dittmar, A.~Yu.~Solynin
\paper Mixed Stekloff eigenvalue problem and new extremal properties of the Gr\"otzsch ring
\inbook Investigations on linear operators and function theory. Part~28
\serial Zap. Nauchn. Sem. POMI
\yr 2000
\vol 270
\pages 51--79
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1327}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1795639}
\zmath{https://zbmath.org/?q=an:1118.35318}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2003
\vol 115
\issue 2
\pages 2119--2134
\crossref{https://doi.org/10.1023/A:1022876518846}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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