Zikai Ye

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math.AP2024

Co-existence of Type II blow-ups with multiple blow-up rates for five-dimensional heat equation with critical nonlinear boundary conditions

Juncheng Wei, Zikai Ye, Xiaoyu Zeng +1

We consider the following five-dimensional heat equation with critical boundary condition \begin{equation*} \partial_t u=Δu \mbox{ \ in \ } \mathbb{R}_+^5\times (0,T) , \quad -\par…

math.AP2023

On Beckner's Inequality for Axially Symmetric Functions on $S^{6}$

Changfeng Gui, Tuoxin Li, Juncheng Wei +1

We prove that axially symmetric solutions to the $Q$ -curvature type problem $$ αP_6 u + 120(1-\frac{e^{6u}}{\int_{\mathbb{S}^6} e^{6u}})=0 \ \ \ \ \ \mbox{on} \ \mathbb{S}^6 $$ mus…

Co-existence of Type II blow-ups with multiple blow-up rates for five-dimensional heat equation with critical nonlinear boundary conditions

On Beckner's Inequality for Axially Symmetric Functions on S6

On Beckner's Inequality for Axially Symmetric Functions on $S^{6}$