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This analysis reveals best constants for Sobolev inequalities involving polyharmonic operators and regularity results.
Our main goal is to explicitly compute the best constant for the Sobolev-type inequality involving the polyharmonic operator obtained in (Analysis and Applications 22, pp. 1417-1446, 2024). To achieve this goal, we also establish both regularity and classification results for a generalized critical polyharmonic equation in the radial setting.
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Oliveira et al. (2025) studied this question.
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