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In this article we consider a special type of degenerate elliptic partialdifferential equations of second order in convex domains that satisfy theinterior sphere condition. We show that any positive viscosity solution $u$ of$-|\nabla u|^\alpha \Delta_p^N u = 1$ has the property that $u^\frac{\alpha +1}{\alpha + 2}$ is a concave function. Secondly we consider positive solutionsof the eigenvalue problem $-|\nabla u|^\alpha \Delta_p^N u = \lambda|u|^{\alpha} u$, in which case $\log u$ turns out to be concave. The methodsprovided include a weak comparison principle and a Hopf-type Lemma.

Power- and Log-concavity of viscosity solutions to some elliptic Dirichlet problems