Concave power solutions of the Dominative $p$-Laplace equation

In this paper, we study properties of solutions of the Dominative $p$-Laplace equation with homogeneous Dirichlet boundary conditions in a bounded convex domain $\mathrm{\Omega }$. For the equation $-{\mathcal{D}}_{p}u=1$, we show that $\sqrt{u}$ is concave, and for the eigenvalue problem $$\mathcal{D}$_p u + \lambda u=0$,weshowthat$\log {u}$ is concave.