Magnetic Steklov operator on differential forms

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.