  We study the generalized boundary value problem for nonnegative solutions of
of $-\Delta u+g(u)=0$ in a bounded Lipschitz domain $\Omega$, when $g$ is
continuous and nondecreasing. Using the harmonic measure of $\Omega$, we define
a trace in the class of outer regular Borel measures. We amphasize the case
where $g(u)=|u|^{q-1}u$, $q>1$. When $\Omega$ is (locally) a cone with vertex
$y$, we prove sharp results of removability and characterization of singular
behavior. In the general case, assuming that $\Omega$ possesses a tangent cone
at every boundary point and $q$ is subcritical, we prove an existence and
uniqueness result for positive solutions with arbitrary boundary trace.
