位移凸性和相边界处的最小前沿
Displacement convexity and minimal fronts at phase boundaries
摘要：
我们表明，某些自由能泛函是不凸的，相对于通常的凸结构，其定义域，是严格凸的位移凸性的意义下，一个自然的变量变换。我们用这一点来证明，在某些情况下，这些泛函的唯一临界点是极小化。这种基于位移凸性的方法使我们能够处理多组分系统以及单组分系统。这些发展产生了新的位移凸泛函的例子，并在多分量设置，联合位移凸泛函。
英文摘要：
We show that certain free energy functionals that are not convex with respect to the usual convex structure on their domain of definition, are strictly convex in the sense of displacement convexity under a natural change of variables. We use this to show that in certain cases, the only critical points of these functionals are minimizers. This approach based on displacement convexity permits us to treat multicomponent systems as well as single component systems. The developments produce new examples of displacement convex functionals, and, in the multi-component setting, jointly displacement convex functionals.
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