Remarks on a Finsler-Laplacian

We investigate elementary properties of a Finsler-Laplacian operator $Q$ that is associated with functionals containing $(H(\nabla u))^2$. Here $H$ is convex and homogeneous of degree 1, and its polar $H^o$ represents a Finsler metric on $\mathbb{R}^n$. In particular we study the Dirichlet problem $-Qu=2n$ on a ball $K^o=\{x\in\mathbb{R}^n : H^o(x)<1\}$ and present a fundamental solution for $Q$, suitable maximum and comparison principles, and a mean value property for solutions of $Qu=0$.