7 papers
The -Laplace equation with a gradient term II: classification in the second critical case
Tian Wu, Jin Yan, Hua Zhu
Let and . 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…
Subcritical limits of a 1D KPZ growth surface with finite moments
Dang-Zheng Liu, Fangzhou Luo, Tian Wu +1
We consider the one-dimensional random growth surface introduced by Adhikari and Chatterjee [AC24], where the height function is defined recursively via the heights at two neighbor…
Spectral Improvements of Geometric Inequalities on Closed Kähler Manifolds
Sayantan Chakraborty, Xiaodong Wang, Tian Wu
Let be a closed Kähler manifold satisfying . We establish improved Liouville theorems for the Euler--Lagrange equations associated with the…
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 -Laplace equations on a closed -dimensional Riemannian manifold with . For $1<p<2…
Classification of positive solutions to a class of Laplace equations with a gradient term
Jingbo Dou, Benfeng Shi, Tian Wu +1
In this paper, we investigate positive solutions to a class of Laplace equations with a gradient term on a complete, connected, and noncompact Riemannian manifold \((M^n,g)\) with…
Liouville theorems for anisotropic -Laplace equations with a semilinear term
Weizhao Liang, Tian Wu, Jin Yan
In this paper, we investigate Liouville theorems for solutions to the anisotropic -Laplace equation $$-Δ_p^H u=-\operatorname{div}(a(\nabla u))=f(u),\quad\text{in }\mathbb{R}^n,…
Classification of positive solutions of critical anisotropic Sobolev equation without the finite volume constraint
Lu Chen, Tian Wu, Jin Yan +1
In this paper, we classify all positive solutions of the critical anisotropic Sobolev equation \begin{equation}\label{0.1} -Δ^{H}_{p}u = u^{p^{*}-1}, \ \ x\in \mathbb{R}^n \end{equ…