In this article, we study the regularity of the boundary of sets minimizing a quasi perimeter with a volume constraint. Here is any open subset of with , is a lower semicontinuous function on sets of finite perimeter satisfying a condition that among all sets of finite perimeter with equal volume. We show that under the condition , any volume constrained minimizer of the quasi perimeter has both interior points and exterior points, and 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 regularity for the reduced boundary of .
Cite this article
Qinglan Xia, Regularity of minimizers of quasi perimeters with a volume constraint. Interfaces Free Bound. 7 (2005), no. 3, pp. 339–352DOI 10.4171/IFB/128