  We study the boundary value problem with measures for (E1) $-\Gd u+g(|\nabla
u|)=0$ in a bounded domain $\Gw$ in $\BBR^N$, satisfying (E2) $ u=\gm$ on
$\prt\Gw$ and prove that if $g\in L^1(1,\infty;t^{-(2N+1)/N}dt)$ is
nondecreasing (E1)-(E2) can be solved with any positive bounded measure. When
$g(r)\geq r^q$ with $q>1$ we prove that any positive function satisfying (E1)
admits a boundary trace which is an outer regular Borel measure, not
necessarily bounded. When $g(r)=r^q$ with $1
