Limiting absorption principle for a hybrid resonance in a two-dimensional cold plasma

Maryna Kachanovska; Étienne Peillon

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arXiv · 2510.15153

Limiting absorption principle for a hybrid resonance in a two-dimensional cold plasma

Maryna Kachanovska·Étienne Peillon

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Abstract

We study a limiting absorption principle for the boundary-value problem describing a hybrid plasma resonance, with a regular coefficient in the principal part of the operator that vanishes on a curve inside the domain and changes its sign across this curve. We prove the limiting absorption principle by establishing a priori bounds on the solution in certain weighted Sobolev spaces. Next, we show that the solution can be decomposed into regular and singular parts. A peculiar property of this decomposition enables us to introduce a radiation-like condition in a bounded domain and to state a well-posed problem satisfied by the limiting absorption solution.

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Maryna Kachanovska, Étienne Peillon. 2025-10-16. Limiting absorption principle for a hybrid resonance in a two-dimensional cold plasma. https://arxiv.org/abs/2510.15153

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