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

Abstract

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 $\mathrm{BV}$. Here, we particularly deal with the autonomous case of convex linear growth functionals.