Magnetic Steklov operator on differential forms

TL;DR

This paper introduces the magnetic Steklov operator on differential forms, establishes its well-posed boundary value problem, explores the failure of the Diamagnetic Inequality, and provides spectral computations for specific Euclidean balls.

Contribution

It presents the first definition of the magnetic Steklov operator on differential forms and analyzes its spectral properties and inequalities.

Findings

Boundary value problem is well-posed.

Diamagnetic Inequality does not always hold.

Spectral computations for 2D and 4D Euclidean balls.

Abstract

In this paper, we introduce the magnetic Steklov operator on differential forms and show that the underlying boundary value problem is well-posed. Moreover, we show that an analogue of the Diamagnetic Inequality does not always hold for this operator, and we present some spectral computations of magnetic Steklov operators for $2$-dimensional and $4$-dimensional balls in Euclidean space.