Isolated singularities for fully nonlinear elliptic equations

Abstract

We obtain Serrin type characterization of isolated singularities for solutions of fully nonlinear uniformly elliptic equations F(D2u)=0. The main result states that any solution to the equation in the punctured ball bounded 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 fundamental 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 expression -P+λ,Λ(D2u), (P-λ,Λ(D2u)) as a measure for viscosity supersolutions (subsolutions) of the corresponding equation. Here P±λ,Λ are the Pucci extremal operators. Show more