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

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

2010-11-03

arxiv.org/abs/1011.0915v1

Mathematics

Analysis of PDEs

13 pages, 3 figures

Scientific paper

In space dimension $n\geq3$, we consider the electromagnetic Schr\"odinger
Hamiltonian $H=(\nabla-iA(x))^2-V$ and the corresponding Helmholtz equation
$(\nabla-iA(x))^2u+u-V(x)u=f \in \mathbb{R}^n$. 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.

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