REGULARITY OF CODIMENSION-1 MINIMIZING CURRENTS UNDER MINIMAL ASSUMPTIONS ON THE INTEGRAND

摘要

In this paper, we investigate the regularity theory of codimension-1 integer rectifiable currents that (almost)-minimize parametric elliptic functionals. While in the non-parametric case it follows by De Giorgi-Nash's Theorem that C-1,C-1 regularity of the integrand is enough to prove C-1,C-alpha regularity of minimizers, the present regularity theory for parametric functionals assume the integrand to be at least of class C-2. In this paper, we fill this gap by proving that C-1,C-1 regularity is enough to show that flat almost-minimizing currents are As a corollary, we also show that the singular set has codimension greater than 2.