Isolated Singularities for Fully Nonlinear Elliptic Equations

By D. Labutin. 2001

52 citations recorded by the source corpus.

Abstract 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 + λ , Λ ( D 2 u ), ( P − λ , Λ ( D 2 u )) as a measure for viscosity supersolutions (subsolutions) of the corresponding equation. Here P ± λ , Λ are the Pucci extremal operators.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/07e562f6406145a5ed5af0ded73ba72a4073c6cb

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Fundamental solutions and liouville type theorems for nonlinear integral operators (2011, methodology): “Fundamental solutions for the extremal Pucci operator (α = 1) were first defined by Labutin [17,18] and were used for the study of removability of singularities for these operators.”