Hua Zhu

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

Let $1<m<n$ and $0<q<m-1$. We classify positive, locally bounded weak solutions of \[-\Delta_m u=u^p|Du|^q\quad\text{in }\mathbb R^n,\qquad p=\frac{m-q}{n-m}\left(n+\frac{q}{m-1-q}\right)-1.\] Every solution is constant or belongs to an explicit family of radial solutions, up to translation and scaling. No global bound...