Abstract
We are devoted to studying the ground states of trapped attractive Bose–Einstein condensates in a bounded domain Ω⊂R2, which can be described by minimizers of L2-critical constraint Gross–Pitaevskii energy functional. It has been shown that there is a threshold a∗>0 such that minimizers exist if and only if the interaction strength a satisfies a<a∗. In present paper, we prove that when the trapping potential V(x) attains its flattest global minimum only at the boundary of Ω, the mass of minimizers must concentrate near the boundary of Ω as a↗a∗. This result extends the work of Luo and Zhu (2019).
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