Mixed Stekloff Eigenvalue Problem and New Extremal Properties of the Grötzsch Ring |
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| Authors: | B. Dittmar A. Yu. Solynin |
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| Affiliation: | (1) Fachbereich Mathematik und Informatik, Halle, Martin-Lüther Universität zu Halle-Wittenberg, Deutschland;(2) St.Petersburg Department of the, Steklov Mathematical Institute, Russia |
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| Abstract: | We study the mixed Stekloff eigenvalue problem in doubly connected domains. Using circular symmetrization and a distortion theorem for conformal mappings of an annulus, we find lower bounds for the first eigenvalue. These bounds are sharp for the Grötzsch ring. We also solve an extremal problem for some polygonal doubly connected domains and prove some results concerning the existence of a closed nodal line. Bibliography: 19 titles. |
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