On Friedrichs-type inequalities in domains rarely perforated along the boundaryReport as inadecuate

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Journal of Inequalities and Applications

, 2011:129

First Online: 05 December 2011Received: 10 March 2011Accepted: 05 December 2011


This article is devoted to the Friedrichs inequality, where the domain is periodically perforated along the boundary. It is assumed that the functions satisfy homogeneous Neumann boundary conditions on the outer boundary and that they vanish on the perforation. In particular, it is proved that the best constant in the inequality converges to the best constant in a Friedrichs-type inequality as the size of the perforation goes to zero much faster than the period of perforation. The limit Friedrichs-type inequality is valid for functions in the Sobolev space H.

AMS 2010 Subject Classification : 39A10; 39A11; 39A70; 39B62; 41A44; 45A05.

KeywordsFriedrichs-type inequalities homogenization perforated along the boundary Electronic supplementary materialThe online version of this article doi:10.1186-1029-242X-2011-129 contains supplementary material, which is available to authorized users.

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Author: Yulia Koroleva - Lars-Erik Persson - Peter Wall

Source: https://link.springer.com/

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