کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
840389 908479 2012 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Improved Poincaré inequalities
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
Improved Poincaré inequalities
چکیده انگلیسی

Although the Hardy inequality corresponding to one quadratic singularity, with optimal constant, does not admit any extremal function, it is well known that such a potential can be improved, in the sense that a positive term can be added to the quadratic singularity without violating the inequality, and even a whole asymptotic expansion can be built, with optimal constants for each term. This phenomenon has not been much studied for other inequalities. Our purpose is to prove that it also holds for the gaussian Poincaré inequality. The method is based on a recursion formula, which allows to identify the optimal constants in the asymptotic expansion, order by order. We also apply the same strategy to a family of Hardy–Poincaré inequalities which interpolate between Hardy and gaussian Poincaré inequalities.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 75, Issue 16, November 2012, Pages 5985–6001
نویسندگان
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