کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8959513 1646323 2018 35 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Minimizers of mass critical Hartree energy functionals in bounded domains
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Minimizers of mass critical Hartree energy functionals in bounded domains
چکیده انگلیسی
We consider L2-constraint minimizers of the mass critical Hartree energy functional with a trapping potential V(x) in a bounded domain Ω of R4. We prove that minimizers exist if and only if the parameter a>0 satisfies a0 is the unique positive solution of −Δu+u−(∫R4u2(y)|x−y|2dy)u=0 in R4. By investigating new analytic methods, the refined limit behavior of minimizers as a↗a⁎ is analyzed for both cases where all the mass concentrates either at an inner point x0 of Ω or near the boundary of Ω, depending on whether V(x) attains its flattest global minimum at an inner point x0 of Ω or not. As a byproduct, we also establish two Gagliardo-Nirenberg type inequalities which are of independent interest.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 265, Issue 10, 15 November 2018, Pages 5177-5211
نویسندگان
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