Regularity of Minimizers of Quasi Perimeters with a Volume Constraint
نویسندگان
چکیده
In this article, we study the regularity of the boundary of sets minimizing a quasi perimeter T (E) = P (E,Ω) + G (E) with a volume constraint. Here Ω is any open subset of Rn with n ≥ 2, G is a lower semicontinuous function on sets of finite perimeter satisfying a condition that G (E) ≤ G (F ) + C |E∆F | among all sets of finite perimeter with equal volume. We show that under the condition β > 1 − 1 n , any volume constrained minimizer E of the quasi perimeter T has both interior points and exterior points, and E is indeed a quasi minimizer of perimeter without the volume constraint. Using a well known regularity result about quasi minimizers of perimeter, we get the classical C1,α regularity for the reduced boundary of E.
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