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math.AP2024
On the Stein-Weiss inequalities and higher-order Caffarelli-Kohn-Nirenberg type inequalities: sharp constants, symmetry of extremal functions
Shengbing Deng, Xingliang Tian
In this paper, we first classify all radially symmetry solutions of the following weighted fourth-order equation \begin{equation*} Δ(|x|^{-γ}Δu)=|x|^γu^{\frac{N+4+3γ}{N-4-γ}},\quad…
math.AP2024
Symmetry breaking of extremals for the high order Caffarelli-Kohn-Nirenberg type inequalities: the singular case
Shengbing Deng, Xingliang Tian
Let us consider the following Caffarelli-Kohn-Nirenberg type inequality \begin{equation}\label{nsckn} \int_{\mathbb{R}^N}|x|^{-β}|\mathrm{div} (|x|^α\nabla u)|^2 \mathrm{d}x \geq \…