Steklov Eigenvalues and Quasiconformal Maps of Simply Connected Planar Domains

被引：0
|
作者：
A. Girouard
R. S. Laugesen
B. A. Siudeja
机构：
[1] Université Laval,Department de Mathematiques et Statistique
[2] University of Illinois,Department of Mathematics
[3] University of Oregon,Department of Mathematics
来源：
Archive for Rational Mechanics and Analysis | 2016年 / 219卷
关键词：
Unit Disk; Trial Function; Isoperimetric Inequality; Regular Polygon; Geometric Quantity;
D O I：
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中图分类号：
学科分类号：
摘要：
We investigate isoperimetric upper bounds for sums of consecutive Steklov eigenvalues of planar domains. The normalization involves the perimeter and scale-invariant geometric factors which measure deviation of the domain from roundness. We prove sharp upper bounds for both starlike and simply connected domains for a large collection of spectral functionals including partial sums of the zeta function and heat trace. The proofs rely on a special class of quasiconformal mappings.
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页码：903 / 936
页数：33
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