vanderWaals-Cahn-Hilliard理论中的稳定相界面
Stable phase interfaces in the van der Waals--Cahn--Hilliard theory
摘要：
证明了扰动参数趋于0的vanderWaals-Cahn-Hilliard能量泛函的稳定临界点的局部一致有界、局部能量有界序列所对应的任一极限界面，由低维嵌入光滑稳定极小超曲面和远离余维至少为7的闭奇异集的嵌入光滑稳定极小超曲面所支撑.这个结果是以前已知的情况下的临界点是局部极小的能量，在这种情况下，极限超曲面是局部面积最小化和它的（归一化）重数是1 a.e.我们的定理使用第一作者早期的工作建立稳定的极限接口作为一个整体varifold，并依赖于最近的一般定理的第二作者的正则性结论，在存在较高的多重性。
英文摘要：
We prove that any limit-interface corresponding to a locally uniformly bounded, locally energy-bounded sequence of stable critical points of the van der Waals--Cahn--Hilliard energy functionals with perturbation parameter tending to 0 is supported by an embedded smooth stable minimal hypersurface in low dimensions and an embedded smooth stable minimal hypersurface away from a closed singular set of co-dimension at least 7 in general dimensions. This result was previously known in case the critical points are local minimizers of energy, in which case the limit-hypersurface is locally area minimizing and its (normalized) multiplicity is 1 a.e. Our theorem uses earlier work of the first author establishing stability of the limit-interface as an integral varifold, and relies on a recent general theorem of the second author for its regularity conclusions in the presence of higher multiplicity.
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