Isolated singularities for fully nonlinear elliptic equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:177

Article

Labutin, DA

关键词: isolated singularities;    viscosity solutions to fully nonlinear elliptic;    equations;   

DOI  :  10.1006/jdeq.2001.3998

来源: Elsevier

【 摘 要 】

We obtain Serrin type characterization of isolated singularities for solutions 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 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-lambda Lambda(+)(D(2)u), (P-lambda Lambda(-)(D(2)u)) as a measure for viscosity supersolutions (subsolutions) of the corresponding equation. Here P-lambda Lambda(+/-) are the Pucci extremal operators. (C) 2001 Academic Press.

【 授权许可】

Free