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 $Ω$. For the equation $-\mathcal{D}_p u= 1$, we show that $\sqrt{u}$ is concave, and for the eigenvalue problem $\mathcal{D}_p u + λu=0$, we show that $\log {u}$ is concave.

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