An optimal Poincaré inequality in <IMG BORDER="0" SRC="/proc/2004-132-01/S0002-9939-03-07004-7/gif-title0/img1.gif" > for convex domains期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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An optimal Poincaré inequality in for convex domains

Authors:	Gabriel Acosta Ricardo G Durá n

Institution:	Instituto de Ciencias, Universidad Nacional de General Sarmiento, J. M. Gutierrez 1150, Los Polvorines, B1613GSX Provincia de Buenos Aires, Argentina ; Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina

Abstract:	For convex domains $\Omega\subset\mathbb{R}^n$ with diameter we prove $\begin{displaymath}\Vert u\Vert _{L^1(\omega)} \le \frac{d}{2} \Vert\nabla u\Vert _{L^1(\omega)} \end{displaymath}$ for any with zero mean value on $\omega$ . We also show that the constant in this inequality is optimal.

Keywords:	Poincar\'e inequalities weighted estimates

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