Magnetic Steklov operator on differential forms

2025/11/10 by Tirumala Chakradhar, Chakradhar, Tirumala, Katie Gittins +5
Computer Science · Mathematics · #53C21 #58J32 #58J50 #58J60 #Advanced Mathematical Modeling in Engineering #Contact Mechanics and Variational Inequalities #Differential Geometry (math.DG) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2511.06877

openalex publication_date 2025/11/10 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28

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.

Citations

• On the magnetic Dirichlet to Neumann operator on the disk -- strong diamagnetism and strong magnetic field limit--
• Magnetic Steklov problem on surfaces
• A note on the magnetic Steklov operator on functions
• Trace formulas for the magnetic Laplacian and Dirichlet to Neumann operator -- Explicit expansions --
• Geometry of the magnetic Steklov problem on Riemannian annuli
• Some recent developments on the Steklov eigenvalue problem
• Isoperimetric inequalities for the magnetic Neumann and Steklov problems with Aharonov-Bohm magnetic potential
• Spectral Invariants of the Magnetic Dirichlet-to-Neumann Map on Riemannian Manifolds
• The diamagnetic inequality for the Dirichlet-to-Neumann operator
• Ricci curvature and eigenvalue estimates for the magnetic Laplacian on manifolds
• On the spectrum of the Dirichlet-to-Neumann operator acting on forms of a Euclidean domain
• Determining a magnetic Schroedinger operator from partial Cauchy data

Related

• A note on the magnetic Steklov operator on functions
• Magnetic Steklov problem on surfaces
• Geometry of the magnetic Steklov problem on Riemannian annuli
• The magnetic formalism; new results
• Magnetic Schroedinger operators and the d-bar equation