Minkowski problem arising from sub-linear elliptic equations

Abstract

For any bounded convex domain \Omega in R^N, we assign a positive finite Borel measure associated with the solution to a su-blinear elliptic equation in \Omega. We prove that this measure is weakly continuous in the sense of measure with respect Hausdorff metric, and the Minkowski problem associated with this measure is uniquely solvable.