Remarks on a Finsler-Laplacian

We investigate elementary properties of a Finsler-Laplacian operator Q that is associated with functionals containing (H (u) ) 2. Here H is convex and homogeneous of degree 1, and its polar H o represents a Finsler metric on R n. In particular we study the Dirichlet problem -Qu = 2n on a ball K o = x 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.