The authors consider the overdetermined boundary value problem \[ \begin{cases} |\nabla u|^\alpha {\mathcal M}_{a,A}(D^2u)+f(u)=0 & \text{in}\;\Omega,\\ u=0 & \text{on}\;\partial\Omega,\\ \partial_{\vec{n}}u=c & \text{on}\;\partial\Omega, \end{cases} \] where \(\alpha>-1\), \(\Omega\) ia a bounded \({\mathcal C}^{2,h}\) domain for some \(0<h<1\), \(\vec{n}\) is the unit outer normal to \(\Omega\), \(c\) is a constant, \({\mathcal M}_{a,A}\) is one of the Pucci operators, and \(f\) is a Hölder continuous function.
They prove that if there exists a non-negative viscosity solution \(u\) of the overdetermined boundary problem above, then either \(u\equiv0\) (and \(c=f(0)=0\)), or \(\Omega\) is a ball and \(u\) is radial (and \(c\neq0\)).