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We study the generalized boundary value problem for (E)\; $-\Deltau+|u|^{q-1}u=0$ in a dihedral domain $\Gw$, when $q>1$ is supercritical. Thevalue of the critical exponent can take only a finite number of valuesdepending on the geometry of $\Gw$. When $\gm$ is a bounded Borel measure in ak-wedge, we give necessary and sufficient conditions in order it be theboundary value of a solution of (E). We also give conditions which ensure thata boundary compact subset is removable. These conditions are expressed in termsof Bessel capacities $B_{s,q'}$ in $\BBR^{N-k}$ where $s$ depends on thecharacteristics of the wedge. This allows us to describe the boundary trace ofa positive solution of (E)

Boundary trace of positive solutions of supercritical semilinear elliptic equations in dihedral domains