The Sharp Ellipticity Threshold for ${\mathrm{W}}^{1,1}$-Regularity

We establish that the ellipticity of the minimal surface integrand is the sharp threshold for ${\mathrm{W}}^{1,1}$-regularity of solutions to the Dirichlet problem on $\mathrm{B}\mathrm{V}$. Here, we particularly deal with the autonomous case of convex linear growth functionals.