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arXiv · 2311.10683

Solvability of Vekua-type periodic operators and applications to classical equations

Alexandre Kirilov·Wagner Augusto Almeida de Moraes·Pedro Meyer Tokoro
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Abstract

In this note, we investigate Vekua-type periodic operators of the form $Pu=Lu-Au-B\bar u$, where $L$ is a constant coefficient partial differential operator. We provide a complete characterization of the necessary and sufficient conditions for the solvability and global hypoellipticity of $P$. As an application, we provide a comprehensive characterization of Vekua-type operators associated with classical wave, heat, and Laplace equations.

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Alexandre Kirilov, Wagner Augusto Almeida de Moraes, Pedro Meyer Tokoro. 2023-11-17. Solvability of Vekua-type periodic operators and applications to classical equations. https://doi.org/10.1016/j.indag.2024.03.001

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