G. A. Chechkin, Yu. O. Koroleva, L.-E. Persson, P. Wall, “A new weighted Friedrichs-type inequality for a perforated domain with a sharp constant”, Eurasian Math. J., 2011, Volume 2, Number 1,Pages <nobr>81

This article is cited in 2 papers

A new weighted Friedrichs-type inequality for a perforated domain with a sharp constant

G. A. Chechkin^ab, Yu. O. Koroleva^ac, L.-E. Persson^c, P. Wall^c

^a Department of Differential Equations, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
^b Narvik University College, Narvik, Norway
^c Department of Mathematics, Luleå University of Technology, Luleå, Sweden

Abstract: We derive a new three-dimensional Hardy-type inequality for a cube for the class of functions from the Sobolev space $H^1$ having zero trace on small holes distributed periodically along the boundary. The proof is based on a careful analysis of the asymptotic expansion of the first eigenvalue of a related spectral problem and the best constant of the corresponding Friedrichs-type inequality.

Keywords and phrases: partial differential equations, functional analysis, spectral theory, homogenization theory, Hardy-type inequalities, Friedrichs-type inequalities.

MSC: 35B27, 39A10, 39A11, 39A70, 39B62, 41A44, 45A05

Received: 11.10.2010

Language: English