Volume 4,  Issue 1, 2003

Article 9

FUNDAMENTAL INEQUALITIES ON FIRMLY STRATIFIED SETS AND SOME APPLICATIONS

SERGE NICAISE AND OLEG M. PENKIN

UNIVERSITÉ DE VALENCIENNES ET DU HAINAUT CAMBRÉSIS
MACS
INSTITUT DES SCIENCES ET TECHNIQUES DE VALENCIENNES
59313 - VALENCIENNES CEDEX 9, FRANCE. 
E-Mail: serge.nicaise@univ-valenciennes.fr

VORONEZH STATE UNIVERSITY
UNIVERSITETSKAJA PL., 1
394000 VORONEZH, RUSSIA.

Received 13 May, 2002; Accepted 11 October, 2002.
Communicated by: M.Z. Nashed

ABSTRACT.   We establish different fundamental inequalities on a class of multistructures, more precisely Poincaré's inequality for second and fourth order (scalar) operators as well as Korn's inequality for the elasticity systems. Some consequences to the corresponding variational problems are deduced.
Key words:
Poincaré's inequality, Korn's inequality, Multistructures.

2000 Mathematics Subject Classification:
35J50, 35R05, 35Q72.

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