Boundary trace of positive solutions of supercritical semilinear elliptic equations in dihedral domains (Q2807108)

The very interesting paper under review deals with generalized boundary value problems for the equation NEWLINE\[NEWLINE -\Delta u+|u|^{q-1}u=0 NEWLINE\]NEWLINE where \(\Omega\subset \mathbb{R}^N\) is a bounded Lipschitz dihedral domain and \(q>1\) is supercritical. The value of the critical exponent can take only a finite number of values depending on the geometry of \(\Omega\). In the case when \(\Omega\) is a \(k\)-wedge, given a bounded Borel measure \(\mu\) on \(\partial\Omega\), the authors give necessary and sufficient conditions in order \(\mu\) to be the boundary value of a solution to the equation considered. Moreover, criteria are provided ensuring that a boundary compact subset is removable. These conditions are expressed in terms of Bessel capacities \(B_{s,q'}\) in \(\mathbb{R}^{N-k}\), where \(s\) depends on the characteristics of the wedge, allowing this way to describe the boundary trace of a positive solution.