Geodesic
Regularity of minimizers of quasi perimeters with a volume constraint
Qinglan Xia1
1University of Texas at Austin, USA
Interfaces and free boundaries, Tome 7 (2005) no. 3, pp. 339-352

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DOI

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∣β among all sets of finite perimeter with equal volume. We show that under the condition β>1−n1​, 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.
DOI : 10.4171/ifb/128
Classification : 35-XX, 65-XX, 76-XX, 92-XX

Qinglan Xia  1

1 University of Texas at Austin, USA 
Qinglan Xia. Regularity of minimizers of quasi perimeters with a volume constraint. Interfaces and free boundaries, Tome 7 (2005) no. 3, pp. 339-352. doi: 10.4171/ifb/128
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     year = {2005},
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     number = {3},
     doi = {10.4171/ifb/128},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/128/}
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