14 papers · 1 filter
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…
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 \…
Gradient stability of Caffarelli-Kohn-Nirenberg inequality involving weighted p-Laplace
Shengbing Deng, Xingliang Tian
The best constant and extremal functions are well known of the following Caffarelli-Kohn-Nirenberg inequality \[ \int_{\mathbb{R}^N}|\nabla u|^p\frac{\mathrm{d}x}{|x|^μ}\geq \mathc…
A note on the Lp-Sobolev inequality
Shengbing Deng, Xingliang Tian
The usual Sobolev inequality in , asserts that for and ,…
Symmetry breaking of extremals for the high order Caffarelli-Kohn-Nirenberg type inequalities
Shengbing Deng, Xingliang Tian
In this paper we give the first result about the precise symmetry and symmetry breaking regions of extremal functions for weighted second-order inequalities. Firstly, based on the…
Classification and non-degeneracy of positive radial solutions for a weighted fourth-order equation and its application
Shengbing Deng, Xingliang Tian
This paper is devoted to radial solutions of the following weighted fourth-order equation \begin{equation*} \mathrm{div}(|x|^α\nabla(\mathrm{div}(|x|^α\nabla u)))=u^{2^{**}_α-1},\q…