论文标题
单孔Modica-Mortola功能及其在Kobayashi的应用 - Warren-练习 - 校准能量
A finer singular limit of a single-well Modica--Mortola functional and its applications to the Kobayashi--Warren--Carter energy
论文作者
论文摘要
在图形收敛下给出了一维空间的单孔模态函数的伽马极限的明确表示，该空间比传统的$ l^1 $ convergence或Conlemgence或收敛。作为一种应用，给出了在材料科学中流行的Kobayashi-Warren-Carter Energy的单一界限的明确表示。还建立了图表收敛下的一些紧凑性。这种公式以及紧凑性，可用于表征最小化器的极限Kobayashi-Warren-Carter能量。为了表征图表收敛下的伽马极限，引入了一个对于一维问题特别有用的新想法。它是该图的弧形长度参数的变量变化，该参数被称为本文中的Arc-Length参数展开。
An explicit representation of the Gamma limit of a single-well Modica--Mortola functional is given for one-dimensional space under the graph convergence which is finer than conventional $L^1$-convergence or convergence in measure. As an application, an explicit representation of a singular limit of the Kobayashi-Warren-Carter energy, which is popular in materials science, is given. Some compactness under the graph convergence is also established. Such formulas, as well as compactness, is useful to characterize the limit of minimizers the Kobayashi-Warren-Carter energy. To characterize the Gamma limit under the graph convergence, a new idea which is especially useful for one-dimensional problem is introduced. It is a change of parameter of the variable by arc-length parameter of its graph, which is called unfolding by the arc-length parameter in this paper.
