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On Dolbeault's conjecture
Juncheng Wei, Zetian Yan, Zikai Ye
We prove sharp improved Sobolev inequalities on , , for antipodally even functions and for axially symmetric functions whose critical density h…
A positive answer to the generalized Chang-Yang conjecture on
Changfeng Gui, Tuoxin Li, Juncheng Wei +1
We prove that for every integer and , Beckner's inequality \[ \fracα{2}\int_{\mathbb{S}^N}u(P_{N}u) dw+(N-1)!\int_{\mathbb{S}^N}u dw-\frac{(N-1)!}{N}\l…
Axially Symmetric Rigidity for a -Curvature-Type Equation on
Changfeng Gui, Tuoxin Li, Juncheng Wei +1
We prove that for every even integer or , every axially symmetric solution to the -curvature-type problem $$ αP_N u + (N-1)!(1-\frac{e^{Nu}}{\int_{\math…
Sharp Beckner's Inequalities for Axially Symmetric Functions on
Changfeng Gui, Tuoxin Li, Juncheng Wei +1
We prove that for every integer and , Beckner's inequality \begin{equation*} \fracα{2}\int_{\mathbb{S}^N}u(P_{N}u) dw+(N-1)!\int_{\mathbb{S}^N}u dw-\fr…
Giga-Kohn-type results for the fully fractional heat equation
Yannick Sire, Juncheng Wei, Ke Wu +1
We consider the semilinear fully fractional heat equation \[ (\partial_t-Δ)^σu = |u|^{p-1}u \quad \text{in } \mathbb{R}^n \times \mathbb{R}_{-}, \qquad 0 < σ< 1. \] For …