The forward problem for the electromagnetic Helmholtz equation with critical singularities

TL;DR

This paper investigates the electromagnetic Helmholtz equation with highly singular potentials, providing new resolvent estimates and applications to spectral measures and evolution solutions.

Contribution

It introduces novel resolvent estimates for the magnetic Schrödinger operator with critical singularities, advancing understanding of its spectral and evolution properties.

Findings

Derived new resolvent bounds for singular potentials

Analyzed spectral measure behavior under strong singularities

Applied results to evolution problem solutions

Abstract

We study the forward problem of the magnetic Schr\"odinger operator with potentials that have a strong singularity at the origin. We obtain new resolvent estimates and give some applications on the spectral measure and on the solutions of the associated evolution problem.