Regularity theory and analysis of singularities
In this part we shall discuss the regularity of boundaries of those sets of finite perimeter which arise as minimizers in some of the variational problems considered so far. The following theorem exemplifies the kind of result we shall obtain. We recall from Section 16.2 that E is a local perimeter minimizer (at scale r0) in some open set A, if spt E = E (recall Remark 16.11) and
whenever EΔF ⊂⊂ B(x, r0) A and x A.
Theorem If n ≥ 2, Ais an open set in n, and E is a local perimeter ...