Abstract
This paper is concerned with the Rellich–Kondrachov Theorem on Groups. We establish some conditions which characterize in a precise manner important properties related to this theorem and the Sobolev spaces on groups involved on it. The main motivation to study the Rellich–Kondrachov Theorem on Groups comes from the Bloch spectral cell equation, which is an eigenvalue-eigenfunction problem associated with the assymptotic limit of the anisotropic Schrödinger equation.
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The author Wladimir Neves has received research grants from CNPq through the grant 308064/2019-4, and also by FAPERJ (Cientista do Nosso Estado) through the grant E-26/201.139/2021. Author Jean Silva has received research grants from CNPq through the Grant 303533/2020-0.
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Ccajma, V., Neves, W. & Silva, J. On a characterization of the Rellich–Kondrachov theorem on groups and the Bloch spectral cell equation. Nonlinear Differ. Equ. Appl. 31, 16 (2024). https://doi.org/10.1007/s00030-023-00905-4
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DOI: https://doi.org/10.1007/s00030-023-00905-4