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- W2949442636 abstract "We study the electromagnetic Helmholtz equation notag (nabla + ib(x))^{2}u(x) + n(x)u(x) = f(x), quad xinRd with the magnetic vector potential $b(x)$ and $n(x)$ a variable index of refraction that does not necessarily converge to a constant at infinity, but can have an angular dependency like $n(x) to n_{infty}(frac{x}{|x|})$ as $|x|toinfty$. We prove an explicit Sommerfeld radiation condition notag int_{Rd} |D u - in_{infty}^{1/2}frac{x}{|x|}u|^{2} frac{dx}{1+|x)} < + infty for solutions obtained from the limiting absorption principle and we also give a new energy estimate notag int_{Rd}| nabla_{omega}n_{infty}(frac{x}{|x|})|^{2}frac{|u|^{2}}{1+|x|} dx < +infty, which explains the main physical effect of the angular dependence of $n$ at infinity and deduces that the energy concentrates in the directions given by the critical points of the potential." @default.
- W2949442636 created "2019-06-27" @default.
- W2949442636 creator A5051005026 @default.
- W2949442636 date "2012-01-02" @default.
- W2949442636 modified "2023-09-27" @default.
- W2949442636 title "Energy concentration and explicit Sommerfeld radiation condition for the electromagnetic Helmholtz equation" @default.
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