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.

29 pages, 3 figures; comments welcome