发表机构
The University of Texas at Austin（德克萨斯大学奥斯汀分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究湿泡沫的等周问题，提出松弛能量处理液体腔室坍缩为零厚度薄膜的情况，证明极小化序列极限的存在性与正则性，并揭示液体体积消失时能量收敛于干泡沫。
AI 中文摘要
湿泡沫是由空气腔室组成的簇，其界面被一个具有规定体积的单一液体腔室所包覆。在相应的等周问题中，液体腔室可能坍缩为零厚度的薄膜，因此极小元不一定存在。我们确定了考虑这种坍缩薄膜的松弛能量，并证明了极小化序列的极限是其极小元。由此得到的紧致性和能量表示定理导致了这些广义极小元的正则性，包括跨越坍缩薄膜的压力平衡定律。最后，当液体体积趋于零时，极小能量收敛到经典干泡沫的极小能量。
英文摘要
A wet foam is a cluster of air chambers whose interfaces are coated by a single liquid chamber of prescribed volume. In the corresponding isoperimetric problem the liquid chamber may collapse onto films of zero thickness, so that minimizers need not exist. We identify the relaxed energy accounting for such collapsed films and prove that limits of minimizing sequences are its minimizers. The resulting compactness and energy representation theorems lead to the regularity of these generalized minimizers, including an equilibrium law for the pressures across collapsed films. Finally, as the liquid volume vanishes, the minimal energies converge to those of the classical dry foam.
