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

2013/09/30 by Moshe Marcus, Marcus, Moshe, Laurent Veron +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1309.7778

To appear Ann. Sc.Norm. Sup. Pisa Cl. Sci. arXiv admin note: substantial text overlap with arXiv:0907.1006

arxiv created 2014/07/02 · arxiv updated 2014/07/03

Abstract

We study the generalized boundary value problem for (E) -Δu+|u|^q-1u=0 in a dihedral domain \Gw, when q>1 is supercritical. The value of the critical exponent can take only a finite number of values depending on the geometry of \Gw. When \gm 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 B_s,q' in \BBR^N-k where s depends on the characteristics of the wedge. This allows us to describe the boundary trace of a positive solution of (E)

Citations

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

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