Tian Wu

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20242026

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math.AP2026

The $m$ -Laplace equation with a gradient term II: classification in the second critical case

Tian Wu, Jin Yan, Hua Zhu

Let $1 < m < n$ and $0 < q < m - 1$ . We classify positive, locally bounded weak solutions of \[-Δ_m u=u^p|Du|^q\quad\text{in }\mathbb R^n,\qquad p=\frac{m-q}{n-m}\left(n+\frac{q}{m-1-q}\righ…

math.AP2026

Liouville theorem for a class of p-Laplace type equations on manifolds

Xi-Nan Ma, Wei Wei, Tian Wu +1

We study a class of $p$ -Laplace equations $Δ_{p} u - λ u^{p - 1} + u^{q - 1} = 0$ on a closed $n$ -dimensional Riemannian manifold $(M, g)$ with $Ric ⩾ (n - 1) g$ . For $1<p<2…

The m-Laplace equation with a gradient term II: classification in the second critical case

Liouville theorem for a class of p-Laplace type equations on manifolds

The $m$ -Laplace equation with a gradient term II: classification in the second critical case