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

Abstract

In space dimension $n\ge 3$, we consider the electromagnetic Schrödinger Hamiltonian $H=(\nabla -iA(x){)}^2-V$ and the corresponding Helmholtz equation $(\nabla -iA(x){)}^{2}u+u-V(x)u=f\in {\mathbb{R}}^n$. 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.

arXiv comment13 pages, 3 figures