On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues |
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Authors: | A Girouard I Polterovich |
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Institution: | (1) Atomic Physics Division, Department of Atomic Physics and Luminescence, Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80–233 Gdańsk, Poland |
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Abstract: | We prove that the Hersch-Payne-Schiffer isoperimetric inequality for the nth nonzero Steklov eigenvalue of a bounded simply connected planar domain is sharp for all n ⩾ 1. The equality is attained in the limit by a sequence of simply connected domains degenerating into a disjoint union of
n identical disks. Similar results are obtained for the product of two consecutive Steklov eigenvalues. We also give a new
proof of the Hersch-Payne-Schiffer inequality for n = 2 and show that it is strict in this case. |
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Keywords: | |
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