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Limit Behavior Of Mass Critical Hartree Minimization Problems With Steep Potential Wells, Yujin Guo, Yong Luo, Zhi-Qiang Wang
Limit Behavior Of Mass Critical Hartree Minimization Problems With Steep Potential Wells, Yujin Guo, Yong Luo, Zhi-Qiang Wang
Mathematics and Statistics Faculty Publications
We consider minimizers of the following mass critical Hartree minimization problem: eλ(N) ≔ inf{u∈H1(ℝd),‖u‖22=N} Eλ(u), where d ≥ 3, λ > 0, and the Hartree energy functional Eλ(u) is defined by Eλ(u)≔∫Rd|∇u(x)|2dx + λ∫Rd g(x)u2(x)dx − 1/2∫Rd∫Rd {u2(x)u2(y)/|x−y|2} dxdy. Here the steep potential g(x) satisfies 0 = g(0) = infℝdg(x) ≤ g(x) ≤ 1 and 1 …