Regularity for radial solutions of degenerate fully nonlinear equations (Q452423)

This paper is concerned with the regularity of radial viscosity solutions of \(F(x,\nabla u, D^2u)=f(|x|)\), where \(f\) is continuous, \(F\) is a fully nonlinear degenerate elliptic operator, homogeneous of degree 1 in the Hessian and homogeneous of degree \(\alpha>-1\) in the gradient. The main results of the paper establish that any radial viscosity solution of the above equation in a ball or in an annulus is of class \(C^1\). Furthermore, if either \(N\leq 3\) or \(N>3\) and \(M\mapsto F(x,p,M)\) is convex or concave, then any solution \(u\) is of class \(C^{1,1/(1+\alpha)}\) and it is \(C^2\) on points where the derivative is nonzero.