Spacelike graphs with prescribed mean curvature

Abstract

We describe all the rotationally symmetric spacelike graphs $G_u=\bigl( x,u(\vert x\vert)\bigr)$ in Minkowsky's space whose mean curvature is a prescribed function $f$ of $u$. In particular, we prove the existence of regular and singular solutions by means of a fixed-point theorem, and we study the global behaviour of solutions in the case $f(u)\cdot u$ does not change sign.