Isolated singularities for fully nonlinear elliptic equations

We obtain Serrin type characterization of isolated singularities for soluti ons of fully nonlinear uniformly elliptic equations F(D(2)u) = 0. The main result states that any solution to the equation in the punctured ball bound ed from one side is either extendable to the solution in the entire ball or can be controlled near the centre of the ball by means of special fundamen tal solutions. In comparison with semi- and quasilinear results the proofs use the viscosity notion of generalised solution rather than distributional or Sobolev weak solutions. We also discuss one way of defining the express ion -P-lambda Lambda(+)(D(2)u), (P-lambda Lambda(-)(D(2)u)) as a measure fo r viscosity supersolutions (subsolutions) of the corresponding equation. He re P-lambda Lambda(+/-) are the Pucci extremal operators. (C) 2001 Academic Press.