Removable singularities for some nonlinear elliptic equations

@article{Brezis1980RemovableSF,
  title={Removable singularities for some nonlinear elliptic equations},
  author={Haim Brezis and Laurent V{\'e}ron},
  journal={Archive for Rational Mechanics and Analysis},
  year={1980},
  volume={75},
  pages={1-6}
}
  • H. Brezis, L. Véron
  • Published 1 March 1980
  • Mathematics
  • Archive for Rational Mechanics and Analysis
then there exists a C 2 function on f2 which coincides with u on f2'. In other words the equation (2) A u + l u f l u = O has the property that any isolated singularity is "removable". When p=(N+2)/(N-2) , this result is a consequence of a theorem of LOEWNER & NIRENBERG (see [2], Theorem 7). We note that the restriction p > N / ( N 2 ) is essential, for if I < p < N / ( N 2 ) there are solutions of (2) with isolated singularities (the full description of such singularities is discussed in [3]). 
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