Spectral asymptotics for magnetic Schr\"odinger operators in domains with corners

TL;DR

This paper derives semiclassical spectral formulas for magnetic Schrödinger operators in two-dimensional domains with corners, extending previous results from smooth to piecewise smooth domains.

Contribution

It extends semiclassical spectral asymptotics for magnetic Schrödinger operators from smooth to cornered domains in two dimensions.

Findings

Semiclassical formulas for eigenvalue sums and counts in cornered domains.

Extension of previous smooth domain results to piecewise smooth geometries.

New mathematical techniques for handling corners in spectral analysis.

Abstract

This paper is on magnetic Schrodinger operators in two dimensional domains with corners. Semiclassical formulas are obtained for the sum and number of eigenvalues. The obtained results extend former formulas for smooth domains in \cite{Fr, FK} to piecewise smooth domains.