Minimizers and best constants for a weighted critical Sobolev inequality involving the polyharmonic operator

2025/05/14 by de Oliveira, José Francisco, Silva, Jeferson
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.09035

Abstract

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.

Citations

• Classification and non-degeneracy of positive radial solutions for a weighted fourth-order equation and its application
• Trudinger-Moser embeddings on weighted Sobolev spaces on unbounded domains
• Sharp Sobolev and Adams–Trudinger–Moser embeddings on weighted Sobolev spaces and their applications
• Classification for positive singular solutions to critical sixth order equations
• A Sharp Adams-Type Inequality for Weighted Sobolev Spaces
• The Brezis-Nirenberg result for the fractional Laplacian
• Existence of solitary waves in higher dimensions

Related

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• Normalized solutions to polyharmonic equations with Hardy-type potentials and exponential critical nonlinearities
• Best Constants in the Hardy-Rellich Inequalities and Related Improvements
• Construction of solutions for the critical polyharmonic equation with competing potentials
• Critical dimensions for polyharmonic operators: The Pucci-Serrin conjecture for solutions of bounded energy