| In this paper we study the special Lagrangian equation and related equations. Special Lagrangian equation originates in the special Lagrangian geometry by Harvey-Lawson [HL1].;In subcritical phases, we construct singular solutions in dimension three and higher. We also convert our counterexamples to the ones for the minimal surface system equation.;In critical and supercritical phases, we derive a priori Hessian estimates in general higher dimensions (n ≥ 4). Our unified approach leads to sharper estimates for previously known three dimensional and convex solution cases. |
