کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4612707 | 1338703 | 2006 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Uniqueness of solutions for a mean field equation on torus
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Uniqueness of solutions for a mean field equation on torus Uniqueness of solutions for a mean field equation on torus](/preview/png/4612707.png)
چکیده انگلیسی
We consider on a two-dimensional flat torus T the following equationΔu+ρ(eu∫Teu−1|T|)=0. When the fundamental domain of the torus is (0,a)×(0,b)(0,a)×(0,b)(a⩾b)(a⩾b), we establish that the constants are the unique solutions wheneverρ⩽{8πifba⩾π4,32baifba⩽π4, and this result is sharp if ba⩾π4. A similar conclusion is obtained for general two-dimensional torus by considering the length of the shortest closed geodesic. These results are derived by comparing the isoperimetric profile of the torus T with the one of the two-dimensional canonical sphere which has same volume as T.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 229, Issue 1, 1 October 2006, Pages 172–185
Journal: Journal of Differential Equations - Volume 229, Issue 1, 1 October 2006, Pages 172–185
نویسندگان
Chang-Shou Lin, Marcello Lucia,