Boundary singularities for weak solutions of semilinear elliptic problems

Details Boundary singularities for weak solutions of semilinear elliptic problems Boundary singularities for weak solutions of semilinear elliptic problems

2007-02-09

arxiv.org/abs/math/0702247v1

Mathematics

Analysis of PDEs

Scientific paper

We construct positive weak solutions of a class of semilinear elliptic
equation which vanish in suitable trace sense on the boundary of a given smooth
bounded N-dimensional domain, but which are singular at prescribed isolated
points of the boundary. Similar constructions are carried out for solutions
which are singular on any given embedded submanifold of the boundary.

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