Non-trapping magnetic fields and Morrey-Campanato estimates for Schroedinger operators

2008/11/18 by Luca Fanelli, Fanelli, Luca
Mathematics · Physics and Astronomy · #35J10 #35L05 #58J45 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.MP #msc:35J10 #msc:35L05 #msc:58J45

paper · pdf · doi:10.48550/arxiv.0811.3011

18 pages

arxiv created 2008/11/18 · openalex publication_date 2008/11/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove some uniform in ε a priori estimates for solutions of the equation (∇-iA)²u-V(x)u+(λ± iε)u=f, λ≥0, ε≠0. The estimates are obtained in terms of Morrey-Campanato norms, and can be used to prove absence of zero-resonances, in a suitable sense, for electromagnetic Hamiltonians. Precise conditions on the size of the trapping component of the magnetic field and the non repulsive component of the electric field are given.

Citations

• Spectral properties of Schrödinger operators and time-decay of the wave functions
• Time decay for solutions of Schr�dinger equations with rough and time-dependent potentials

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