Applied Maths Seminar: Cirstea -- Semilinear elliptic equations with isolated singularities

We consider semilinear elliptic equations in a punctured domain and give a complete
classification of isolated singularities of positive solutions when the nonlinearity is
regularly varying at infinity with index greater than 1.  We extend an important result
of Veron (1981, 1986) (also proved by Brezis and Oswald in 1987) for the power case,
whose study was motivated by the understanding of some physical phenomena (in connection
with Thomas--Fermi theory).  It remained an open question whether this type of result is
valid in a more general framework.  The difficulties of this problem required the
development of new techniques, which we provide using Karamata’s theory of regular
variation.  Our approach offers a third alternative proof in the literature even in the
special power case treated by Veron.  (This is joint work with Y.  Du from UNE) 

http://www.maths.usyd.edu.au/u/AppliedSeminar/abstracts/2008/cirstea.html