Radó type removability result for fully nonlinear equations

Abstract

We consider the removability of a level set for solutions to fully nonlinear elliptic and parabolic equations. We prove that if a $C^1$ function $u$ is a viscosity solution to the fully nonlinear equation $F(x,u,Du,D^2u)=0$ or $u_t + F(t,x,u,Du,D^2u)=0$ in a domain outside the zero-level set of $u$, then $u$ is indeed a viscosity solution to the same equation in the whole domain, under some hypotheses on $F$. We also establish the removability result for singular fully nonlinear equations.