二维哑铃形畴的几何诱导相变
Geometrically induced phase transitions in two-dimensional dumbbell-shaped domains
摘要：
我们继续Morini&Slastikov（2012）中开始的二维非凸变分问题的分析，其动机是对薄颈捕获的磁畴壁的研究。主要的重点是极端的几何结构上的局部极小代表两个不同的恒定相位之间的过渡的影响。我们在这里解决的情况下，一般的非对称哑铃形域与一个小的收缩和一般的多阱电位。我们的主要结果关注的存在性和唯一性的非常数局部极小，他们的完整分类的情况下凸块，和完整的描述，其渐近行为，作为收缩的大小趋于零。
英文摘要：
We continue the analysis, started in Morini&Slastikov (2012), of a two-dimensional non-convex variational problem, motivated by studies on magnetic domain walls trapped by thin necks. The main focus is on the impact of extreme geometry on the structure of local minimizers representing the transition between two different constant phases. We address here the case of general non-symmetric dumbbell-shaped domains with a small constriction and general multi-well potentials. Our main results concern the existence and uniqueness of non-constant local minimizers, their full classification in the case of convex bulks, and the complete description of their asymptotic behavior, as the size of the constriction tends to zero.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
