This is the equation for a function $u(x,y)$ whose graph is a minimal surface (its mean curvature is $0$):
$$(1+u_x^2)u_{yy}-2u_xu_yu_{xy}+(1+u_y^2)u_{xx}=0$$
My question is if there are non-smooth o distributional solutions to this equation, so there can be non-smooth minimal surfaces; for example, surfaces given by a step function or similar.