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.
Archive for Rational Mechanics and Analysis
- Pub Date:
- February 2016
- Mathematics - Spectral Theory;
- Mathematics - Analysis of PDEs;
- Primary 35P15. Secondary 35J20;