  We study the generalized boundary value problem for nonnegative solutions of
$-\Delta u+g(u)=0$ in a bounded Lipschitz domain $\Gw$, when $g$ is continuous
and nondecreasing. Using the harmonic measure of $\Gw$, 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 $\Gw$ is (locally) a cone with vertex $y$, we
prove sharp results of removability and characterization of singular behavior.
In the general case, assuming that $\Gw$ 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. We obtain sharp
results involving Besov spaces with negative index on k-dimensional edges and
apply our results to the characterization of removable sets and good measures
on the boundary of a polyhedron.

Analysis of PDEs