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math.AP2023★ 1 cited
Stability of the Caffarelli-Kohn-Nirenberg inequality: the existence of minimizers
Juncheng Wei, Yuanze Wu
In this paper, we consider the following variational problem: \begin{eqnarray*} \inf_{u\in D^{1,2}_a(\bbr^N)\backslash\mathcal{Z}}\frac{\|u\|^2_{D^{1,2}_a(\bbr^N)}-C_{a,b,N}^{-1}\|…
math.AP2023★ 1 cited
Long-time dynamics for the energy critical heat equation in
Zaizheng Li, Qidi Zhang, Yifu Zhou +1
We investigate the long-time behavior of global solutions to the energy critical heat equation in \begin{equation*} \begin{cases} \pp_t u=Δu+|u|^{\frac{4}{3}} u ~&\mbox{ in }…
math.AP2023
On Beckner's Inequality for Axially Symmetric Functions on
Changfeng Gui, Tuoxin Li, Juncheng Wei +1
We prove that axially symmetric solutions to the -curvature type problem $$ αP_6 u + 120(1-\frac{e^{6u}}{\int_{\mathbb{S}^6} e^{6u}})=0 \ \ \ \ \ \mbox{on} \ \mathbb{S}^6 $$ mus…