Fundamental Solutions of Homogeneous Fully Nonlinear Elliptic Equations

@inproceedings{Armstrong2012FundamentalSO,
title={Fundamental Solutions of Homogeneous Fully Nonlinear Elliptic Equations},
author={S Armstrong and Charles K. Smart},
year={2012}
}

We prove the existence of two fundamental solutions Φ and Φ̃ of the PDE F (DΦ) = 0 in R \ {0} for any positively homogeneous, uniformly elliptic operator F . Corresponding to F are two unique scaling exponents α∗, α̃∗ > −1 which describe the homogeneity of Φ and Φ̃. We give a sharp characterization of the isolated singularities and the behavior at infinity of a solution of the equation F (D2u) = 0, which is bounded on one side. A Liouville-type result demonstrates that the two fundamental… CONTINUE READING