Minimal partition problems consist in finding a partition of a domain into a given number of components in order to minimize a geometric criterion. In applicative fields such as image processing or continuum mechanics, it is standard to incorporate in this objective an interface energy that accounts for the lengths of the interfaces between components. The present work is focused on the theoretical and numerical treatment of minimal partition problems with such interface energies. The considered approach is based on a $\Gamma$-convergence approximation combined with convex analysis techniques.

中文翻译：

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界面能量的变分近似及其应用

最小的分区问题在于找到将一个域划分为给定数量的组件，以最小化几何准则。在诸如图像处理或连续介质力学之类的应用领域中，标准是在该目标中并入界面能量，该界面能量考虑了部件之间的界面的长度。目前的工作集中在用这种界面能最小分配问题的理论和数值处理上。所考虑的方法基于结合了凸分析技术的$ \ Gamma $收敛逼近。