L^p-L^q estimates for Electromagnetic Helmholtz equation

2010/11/03 by Andoni García, Garcia, Andoni
Mathematics · #35J10 #35L05 #58J45 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1011.0915

openalex publication_date 2010/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In space dimension n≥3, we consider the electromagnetic Schrödinger Hamiltonian H=(∇-iA(x))²-V and the corresponding Helmholtz equation (∇-iA(x))²u+u-V(x)u=f ∈ ℝⁿ. We extend the well known L^p-L^q estimates for the solution of the free Helmholtz equation to the case when the electromagnetic hamiltonian H is considered.

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