Let E⊂Rn be a quasi minimizer of perimeter, that is, a set such that P(E, Bρ(x))≤(1+ω(ρ))P(F,Bρ(x)) for all variations F with FΔE⊂⊂ Bρ(x) and for a given function ω with limρ→0ω(ρ)=0. We prove that, up to a closed set with dimension at most n−8, for all α<1α<1 the set ∂E is an (n−1)-dimensional C0,α manifold. This result is obtained combining the De Giorgi and Reifenberg regularity theories for area minimizers. Moreover we prove that, in the case n=2, ∂E is a bi-lipschitz curve.
Partial regularity for quasi minimizers of perimeter
PAOLINI, EMANUELE
1999-01-01
Abstract
Let E⊂Rn be a quasi minimizer of perimeter, that is, a set such that P(E, Bρ(x))≤(1+ω(ρ))P(F,Bρ(x)) for all variations F with FΔE⊂⊂ Bρ(x) and for a given function ω with limρ→0ω(ρ)=0. We prove that, up to a closed set with dimension at most n−8, for all α<1α<1 the set ∂E is an (n−1)-dimensional C0,α manifold. This result is obtained combining the De Giorgi and Reifenberg regularity theories for area minimizers. Moreover we prove that, in the case n=2, ∂E is a bi-lipschitz curve.File in questo prodotto:
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