For the sigma-2 Hessian equation with positive C^1,1 right-hand side, interior Hessian estimates hold in dimension 4, and in n at least 5 under a dynamic semi-convexity condition.
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Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4
For the sigma-2 Hessian equation with positive C^1,1 right-hand side, interior Hessian estimates hold in dimension 4, and in n at least 5 under a dynamic semi-convexity condition.