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31 December 2001 Factor spaces and implications on Kirchhoff equations with clamped boundary conditions
Irena Lasiecka, Roberto Triggiani
Abstr. Appl. Anal. 6(8): 441-488 (31 December 2001). DOI: 10.1155/S1085337501000586


We consider mixed problems for the Kirchhoff elastic and thermoelastic systems, subject to boundary control in the clamped boundary conditions BC (clamped control). If w denotes the elastic displacement and θ the temperature, we establish sharp regularity of {w,wt,wtt} in the elastic case, and of {w,wt,wtt,θ} in the thermoelastic case. Our results complement those by Lagnese and Lions (1988), where sharp (optimal) trace regularity results are obtained for the corresponding boundary homogeneous cases. The passage from the boundary homogeneous cases to the corresponding mixed problems involves a duality argument. However, in the present case of clamped BC, and only in this case, the duality argument in question is both delicate and technical. In this respect, the clamped BC are “exceptional” within the set of canonical BC (hinged, clamped, free BC). Indeed, it produces new phenomena which are accounted for by introducing new, untraditional factor (quotient) spaces. These are critical in describing both interior regularity and exact controllability of mixed elastic and thermoelastic Kirchhoff problems with clamped controls.


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Irena Lasiecka. Roberto Triggiani. "Factor spaces and implications on Kirchhoff equations with clamped boundary conditions." Abstr. Appl. Anal. 6 (8) 441 - 488, 31 December 2001.


Published: 31 December 2001
First available in Project Euclid: 13 April 2003

zbMATH: 1006.35018
MathSciNet: MR1880989
Digital Object Identifier: 10.1155/S1085337501000586

Primary: 35-XX , 47-XX
Secondary: 93-xx

Rights: Copyright © 2001 Hindawi

Vol.6 • No. 8 • 31 December 2001
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