L^p-L^q estimates for Electromagnetic Helmholtz equation. Singular potentials

2013/10/09 by Andoni García, García, Andoni
Mathematics · #35J10 #35L05 #58J45 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory in Mathematical Physics #math.AP #msc:35J10 #msc:35L05 #msc:58J45

paper · pdf · doi:10.48550/arxiv.1310.2457

25 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1011.0915; and text overlap with arXiv:1104.4237 by other authors

arxiv created 2013/10/09 · openalex publication_date 2013/10/09 · arxiv updated 2013/10/10 · 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 in ℝⁿ, where the magnetic and electric potentials are allowed to have singularities at the origin and decay at infinity. 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. This work extends the results that appear in \citeG.

Citations

• L^p-L^q estimates for Electromagnetic Helmholtz equation
• Limiting absorption principle for the electromagnetic Helmholtz equation with singular potentials

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