2024/10/06 by Shengbing Deng, Deng, Shengbing, Xingliang Tian +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2410.04530
openalex publication_date 2024/10/06 · openalex created_date 2024/10/12 · openalex updated_date 2026/07/28
In this paper, we first classify all radially symmetry solutions of the following weighted fourth-order equation Δ(|x|-γΔu)=|x|γu(N+4+3γ)/(N-4-γ), u≥ 0 in ℝN, where N≥ 5, -2<γ<0. Then we derive the sharp Stein-Weiss inequality and standard second-order Caffarelli-Kohn-Nirenberg inequality with radially symmetry extremal functions. Moreover, by using standard spherical decomposition, we derive a sharp weighted Rellich-Sobolev inequality. Furthermore, we establish the sharp second-order Caffarelli-Kohn-Nirenberg type inequalities with two variables which have radially symmetry extremal functions. Finally, we derive the weak form Hardy-Rellich inequalities with sharp constants.