Resumen de Boundary trace of positive solutions of supercritical semilinear elliptic equations in dihedral domains
We study the generalized boundary value problem for (E) −∆u + |u|q−1u = 0 in a dihedral domain Ω, when q > 1 is supercritical. The value of the critical exponent can take only a finite number of values depending on the geometry of Ω. When μ is a bounded Borel measure in a k-wedge, we give necessary and sufficient conditions in order it be the boundary value of a solution of (E). We also give conditions which ensure that a boundary compact subset is removable. These conditions are expressed in terms of Bessel capacities Bs,q0 in RN−k where s depends on the characteristics of the wedge. This allows us to describe the boundary trace of a positive solution of (E).
