On Schr\"odinger operators with oblique transmission conditions on non-smooth curves

TL;DR

This paper extends the analysis of Schr"odinger operators with oblique transmission conditions from smooth to Lipschitz curves, broadening the applicability of the mathematical framework to less regular geometries.

Contribution

It generalizes existing results on Schr"odinger operators with oblique transmission conditions to include Lipschitz curves, which are less smooth than previously considered.

Findings

Extended the analysis to Lipschitz curves

Maintained key spectral properties in the less smooth setting

Provided new mathematical tools for non-smooth geometries

Abstract

In a recent paper Behrndt, Holzmann, and Stenzel introduced a new class of two-dimensional Schr\"odinger operators with oblique transmissions along smooth curves. We extend most components of this analysis to the case of Lipschitz curves.