REMOVING SINGULARITIES FOR FULLY NONLINEAR PDES

We show removability of half-line singularities for viscosity solutions of fully nonlinear elliptic PDEs which have classical density and a Jacobi inequality. An example of such a PDE is the Monge-Ampère equation, and the original proof follows from Caffarelli [Ann. of Math. (2) 131 (1990), pp. 129–134]. Other examples are the minimal surface and special Lagrangian equations. The present paper’s quick doubling proof combines Savin’s small perturbation theorem with the Jacobi inequality. The method more generally removes singularities satisfying the single side condition.