Steklov eigenvalues and quasiconformal maps of simply connected planar domains
Spectral Theory
2016-01-27 v1 Analysis of PDEs
Abstract
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.
Keywords
Cite
@article{arxiv.1412.8073,
title = {Steklov eigenvalues and quasiconformal maps of simply connected planar domains},
author = {A. Girouard and R. S. Laugesen and B. A. Siudeja},
journal= {arXiv preprint arXiv:1412.8073},
year = {2016}
}