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Geometric regularity for semi-convex viscosity solutions to the special Lagrangian equation
We prove that the gradient graph of any $W^{2,1}$ semi-convex viscosity solution to the three-dimensional subcritical special Lagrangian equation is area-minimizing and smooth. Furthermore, we prove the smoothness of $W^{2,1}\cap C^{1,1/3+}$ semi-convex viscosity solutions. This yields progress on t
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