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On isoperimetric inequalities for single layer potentials


Author: Seyed M. Zoalroshd
Journal: Proc. Amer. Math. Soc. 145 (2017), 323-326
MSC (2010): Primary 47G40; Secondary 35P99, 35S15
DOI: https://doi.org/10.1090/proc/13236
Published electronically: July 12, 2016
MathSciNet review: 3565383
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Abstract: We show that among all rectangles of given perimeter, the square is a minimizer of the Schatten $ p-$norms of the single layer potentials. We also prove that the equilateral triangle is a minimizer of the Schatten $ p-$norms of the single layer potentials over triangles of equal perimeter.


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Additional Information

Seyed M. Zoalroshd
Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620
Email: szoalros@mail.usf.edu

DOI: https://doi.org/10.1090/proc/13236
Keywords: Isoperimetric inequality, single layer potential, Purkiss principle
Received by editor(s): February 15, 2016
Received by editor(s) in revised form: March 28, 2016
Published electronically: July 12, 2016
Communicated by: Michael Hitrik
Article copyright: © Copyright 2016 American Mathematical Society