Logarithmic Refinements of a Power Weighted Hardy--Rellich-Type Inequality

2024/07/06 by Fritz Gesztesy, Gesztesy, Fritz, Michael M. H. Pang +3 · 1 citation
Mathematics · #35J30 #47F05 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 35A23 #Secondary: 47A63

paper · pdf · doi:10.48550/arxiv.2407.05212

openalex publication_date 2024/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The principal purpose of this note is to prove a logarithmic refinement of the power weighted Hardy--Rellich inequality on n-dimensional balls, valid for the largest variety of underlying parameters and for all dimensions n ∈ ℕ, n≥ 2.

Cited by

• An elementary approach to integral inequalities involving higher order derivatives

Related

• Factorizations and Power Weighted Rellich and Hardy--Rellich-Type Inequalities
• A Sequence of Weighted Birman-Hardy-Rellich Inequalities with Logarithmic Refinements
• Optimal Power-Weighted Birman--Hardy--Rellich-type Inequalities on Finite Intervals and Annuli
• Weighted Hardy-Rellich type inequalities: improved best constants and symmetry breaking
• A curl-free improvement of the Rellich-Hardy inequality with weight