Open Access

On the Precise Asymptotics of the Constant in Friedrich's Inequality for Functions Vanishing on the Part of the Boundary with Microinhomogeneous Structure

Journal of Inequalities and Applications20082007:034138

DOI: 10.1155/2007/34138

Received: 3 April 2007

Accepted: 23 October 2007

Published: 17 January 2008

Abstract

We construct the asymptotics of the sharp constant in the Friedrich-type inequality for functions, which vanish on the small part of the boundary https://static-content.springer.com/image/art%3A10.1155%2F2007%2F34138/MediaObjects/13660_2007_Article_1696_IEq1_HTML.gif . It is assumed that https://static-content.springer.com/image/art%3A10.1155%2F2007%2F34138/MediaObjects/13660_2007_Article_1696_IEq2_HTML.gif consists of https://static-content.springer.com/image/art%3A10.1155%2F2007%2F34138/MediaObjects/13660_2007_Article_1696_IEq3_HTML.gif pieces with diameter of order https://static-content.springer.com/image/art%3A10.1155%2F2007%2F34138/MediaObjects/13660_2007_Article_1696_IEq4_HTML.gif . In addition, https://static-content.springer.com/image/art%3A10.1155%2F2007%2F34138/MediaObjects/13660_2007_Article_1696_IEq5_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2007%2F34138/MediaObjects/13660_2007_Article_1696_IEq6_HTML.gif as https://static-content.springer.com/image/art%3A10.1155%2F2007%2F34138/MediaObjects/13660_2007_Article_1696_IEq7_HTML.gif .

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Authors’ Affiliations

(1)
Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow Lomonosov State University
(2)
Department of Mathematics, Luleå University of Technology

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Copyright

© G. A. Chechkin et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.