A new weighted Friedrichs-type inequality for a~perforated domain with a~sharp constant
Eurasian mathematical journal, Tome 2 (2011) no. 1, pp. 81-103
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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.
@article{EMJ_2011_2_1_a3,
author = {G. A. Chechkin and Yu. O. Koroleva and L.-E. Persson and P. Wall},
title = {A new weighted {Friedrichs-type} inequality for a~perforated domain with a~sharp constant},
journal = {Eurasian mathematical journal},
pages = {81--103},
publisher = {mathdoc},
volume = {2},
number = {1},
year = {2011},
language = {en},
url = {http://geodesic.mathdoc.fr/item/EMJ_2011_2_1_a3/}
}
TY - JOUR AU - G. A. Chechkin AU - Yu. O. Koroleva AU - L.-E. Persson AU - P. Wall TI - A new weighted Friedrichs-type inequality for a~perforated domain with a~sharp constant JO - Eurasian mathematical journal PY - 2011 SP - 81 EP - 103 VL - 2 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/EMJ_2011_2_1_a3/ LA - en ID - EMJ_2011_2_1_a3 ER -
%0 Journal Article %A G. A. Chechkin %A Yu. O. Koroleva %A L.-E. Persson %A P. Wall %T A new weighted Friedrichs-type inequality for a~perforated domain with a~sharp constant %J Eurasian mathematical journal %D 2011 %P 81-103 %V 2 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/EMJ_2011_2_1_a3/ %G en %F EMJ_2011_2_1_a3
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 mathematical journal, Tome 2 (2011) no. 1, pp. 81-103. http://geodesic.mathdoc.fr/item/EMJ_2011_2_1_a3/