Gradient estimates and Harnack inequalities for solutions to the minimal surface equation (Q5926042)

The author derives two new estimates for the gradient of solutions to the minimal surface equation in any dimension. Here the gradient is controlled by the area of the graph of the solution or by the integral of it. These estimates and a theorem on description of generalized solutions to the minimal surface equation are obtained as straightforward consequences of a Harnack type inequality proved by \textit{E. Bombieri} and \textit{E. Giusti} [Invent. Math. 15, 24-46 (1972; Zbl 0227.35021)].