کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6415121 1334946 2014 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Trudinger-Moser inequality with remainder terms
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Trudinger-Moser inequality with remainder terms
چکیده انگلیسی

The paper gives the following improvement of the Trudinger-Moser inequality:(0.1)sup∫Ω|∇u|2dx−ψ(u)⩽1,u∈C0∞(Ω)∫Ωe4πu2dx<∞,Ω∈R2, related to the Hardy-Sobolev-Mazya inequality in higher dimensions. We show (0.1) with ψ(u)=∫ΩV(x)u2dx for a class of V>0 that includesV(r)=14r2(log1r)2max{log1r,1}, which refines two previously known cases of (0.1) proved by Adimurthi and Druet [2] and by Wang and Ye [23]. In addition, we verify (0.1) for ψ(u)=λ‖u‖p2, as well as give an analogous improvement for the Onofri-Beckner inequality for the unit disk (Beckner [6]).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 266, Issue 1, 1 January 2014, Pages 55-66
نویسندگان
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