Half-line singularities of viscosity solutions are removable for fully nonlinear elliptic PDEs with a Jacobi inequality, proven by a doubling argument; the single-side version is new.
Hessian estimates for the sigma-2 equation in dimension four
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abstract
We derive a priori interior Hessian estimates and interior regularity for the $\sigma_2$ equation in dimension four. Our method provides respectively a new proof for the corresponding three dimensional results and a Hessian estimate for smooth solutions satisfying a dynamic semi-convexity condition in higher $n\ge 5$ dimensions.
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Removing singularities for fully nonlinear PDEs
Half-line singularities of viscosity solutions are removable for fully nonlinear elliptic PDEs with a Jacobi inequality, proven by a doubling argument; the single-side version is new.