On the connectivity of boundaries of sets minimizing perimeter subject to a volume constraint
The authors study the problem of locally minimizing perimeter within a given bounded domain \(\Omega\) in \textbf{R}\(^n\) subject to a volume constraint. The main result of the paper asserts that if \(\Omega\) is convex then the boundary of any local minimizer is connected. Several interesting applications in the theory of isoperimetric inequalities or in variational problems related to phase transitions are given.
scientific article; zbMATH DE number 1295158