English

Limiting absorption principle for the electromagnetic Helmholtz equation with singular potentials

Analysis of PDEs 2013-09-12 v4

Abstract

We study the following Helmholtz equation (+iA(x))2u+V1(x)u+V2(x)u+λu=f(x) (\nabla +iA(x))^{2} u+ V_{1}(x) u + V_{2}(x) u + \lambda u = f(x) in Rd\mathbb{R}^d with magnetic and electric potentials that are singular at the origin and decay at infinity. We prove the existence of a unique solution satisfying a suitable Sommerfeld radiation condition, together with some a priori estimates. We use the limiting absorption method and a multiplier technique of Morawetz type.

Cite

@article{arxiv.1104.4237,
  title  = {Limiting absorption principle for the electromagnetic Helmholtz equation with singular potentials},
  author = {Miren Zubeldia},
  journal= {arXiv preprint arXiv:1104.4237},
  year   = {2013}
}
R2 v1 2026-06-21T17:57:18.848Z