Weighted Hardy-Rellich type inequalities: improved best constants and symmetry breaking

2024/06/22 by Cristian Cazacu, Cazacu, Cristian, Irina Fidel +1
Mathematics · #34A40 #34K38 #35A23 #35B09 #35Q40 #35R45 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2406.15792

openalex publication_date 2024/06/22 · openalex created_date 2024/06/26 · openalex updated_date 2026/07/28

Abstract

When studying the weighted Hardy-Rellich inequality in L² with the full gradient replaced by the radial derivative the best constant becomes trivially larger or equal than in the first situation. Our contribution is to determine the new sharp constant and to show that for some part of the weights is strictly larger than before. In some cases we emphasize that the extremals functions of the sharp constant are not radially symmetric.

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