Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4
Abstract
We derive a priori interior Hessian estimates and regularity for the sigma-2 Hessian equation σ2(D2u)=f(x,u,Du) with positive C1,1 right hand side in dimension 4. In higher dimensions, the same result holds under an additional dynamic semi-convexity condition on solutions. This generalizes Qiu's and Shankar-Yuan's results.
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