Higher regularity theorems
When dealing with local perimeter minimizers, volume-constrained perimeter minimizers, and minimizers in prescribed mean curvature problems, the C1,-regularity theory from the previous chapters provides only preliminary information on the actual degree of regularity of reduced boundaries. In Section 27.2 we prove some higher regularity theorems, which are based on the fruitful connection between Euler-Lagrange equations for variational integrals and elliptic equations in divergence form presented in Section 27.1.
27.1 Elliptic equations for derivatives of Lipschitz minimizers
A convex function is called locally ...