English

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

Analysis of PDEs 2010-11-04 v1

Abstract

In space dimension n3n\geq3, we consider the electromagnetic Schr\"odinger Hamiltonian H=(iA(x))2VH=(\nabla-iA(x))^2-V and the corresponding Helmholtz equation (iA(x))2u+uV(x)u=fRn(\nabla-iA(x))^2u+u-V(x)u=f \in \mathbb{R}^n. We extend the well known LpL^p-LqL^q estimates for the solution of the free Helmholtz equation to the case when the electromagnetic hamiltonian HH is considered.

Cite

@article{arxiv.1011.0915,
  title  = {$L^p$-$L^q$ estimates for Electromagnetic Helmholtz equation},
  author = {Andoni Garcia},
  journal= {arXiv preprint arXiv:1011.0915},
  year   = {2010}
}

Comments

13 pages, 3 figures

R2 v1 2026-06-21T16:38:28.205Z