کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5774118 | 1413545 | 2017 | 22 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Remarks on endpoint Strichartz estimates for Schrödinger equations with the critical inverse-square potential
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
The purpose of this paper is to study the validity of global-in-time Strichartz estimates for the Schrödinger equation on Rn, nâ¥3, with the negative inverse-square potential âÏ|x|â2 in the critical case Ï=(nâ2)2/4. It turns out that the situation is different from the subcritical case Ï<(nâ2)2/4 in which the full range of Strichartz estimates is known to be hold. More precisely, splitting the solution into the radial and non-radial parts, we show that (i) the radial part satisfies a weak-type endpoint estimate, which can be regarded as an extension to higher dimensions of the endpoint Strichartz estimate with radial data for the two-dimensional free Schrödinger equation; (ii) other endpoint estimates in Lorentz spaces for the radial part fail in general; (iii) the non-radial part satisfies the full range of Strichartz estimates.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 263, Issue 7, 5 October 2017, Pages 3832-3853
Journal: Journal of Differential Equations - Volume 263, Issue 7, 5 October 2017, Pages 3832-3853
نویسندگان
Haruya Mizutani,