Partial regularity for Lipschitz solutions to the minimal surface system

Abstract

In this paper, we study the regularity of several notions of Lipschitz solutions to the minimal surface system with an emphasis on partial regularity results. These include stationary solutions, integral weak solutions, and viscosity solutions. We also prove an interior gradient estimate for classical solutions to the system using the maximum principle, assuming the area-decreasing condition and that all but one component have small infinity norm.