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In this talk,I will present a variational model related to optimal mass transportation. It is motivated by the study of the formation of mud cracking. We study the regularity of the boundary of sets minimizing a quasi perimeter $T(E) =P( E,\Omega ) +G(E)$ with a volume constraint. Here $\Omega $ is any open subset of R^n with n>=2, $G$ is a lower semicontinuous function on sets of finite perimeter satisfying a condition that $G(E)\leq G(F) +C| E\Delta F|^{\beta }$ among all sets of finite perimeter with equal volume. We show that under the condition $\beta >1-1/n$, 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 $C^{1,\alpha }$ regularity for the reduced boundary of $E$.