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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 continuousand nondecreasing. Using the harmonic measure of $\Gw$, we define a trace inthe 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 $y$, weprove sharp results of removability and characterization of singular behavior.In the general case, assuming that $\Gw$ possesses a tangent cone at everyboundary point and $q$ is subcritical, we prove an existence and uniquenessresult for positive solutions with arbitrary boundary trace. We obtain sharpresults involving Besov spaces with negative index on k-dimensional edges andapply our results to the characterization of removable sets and good measureson the boundary of a polyhedron.

Boundary trace of positive solutions of semilinear elliptic equations in Lipschitz domains