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arXiv · 1011.0915

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

Andoni Garcia
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Abstract

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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Andoni Garcia. 2010-11-03. $L^p$-$L^q$ estimates for Electromagnetic Helmholtz equation. https://arxiv.org/abs/1011.0915

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