Ke Wu

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20112026

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math.AP2026

Small-energy regularity for stationary weak solutions of the Liouville equation

Haotong Fu, Kelei Wang, Wei Wang +1

We establish small-energy regularity for stationary weak solutions of the Liouville equation $- Δ u = e^{u}$ in every dimension. It solves a problem left open in Da Lio [Commun. Partia…

math.AP2026

Stable De Giorgi conjecture of the Allen--Cahn equation in $R^{3}$

Yong Liu, Tianci Luo, Kelei Wang +3

We prove that every bounded stable entire solution $v$ of the Allen--Cahn equation in $R^{3}$ is one-dimensional. As a consequence, the full De Giorgi conjecture in $R^{4}$ i…

math.AP2026

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 $n \leq 2 σ$ …

Small-energy regularity for stationary weak solutions of the Liouville equation

Stable De Giorgi conjecture of the Allen--Cahn equation in R3

Giga-Kohn-type results for the fully fractional heat equation

Stable De Giorgi conjecture of the Allen--Cahn equation in $R^{3}$