Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 196956, 15 pages
Research Article

Maximal Regularity for Flexible Structural Systems in Lebesgue Spaces

1Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago, Chile
2Departamento de Matemática, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile
3Departamento de Matemática, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Ñuñoa, Santiago, Chile

Received 9 August 2009; Accepted 13 January 2010

Academic Editor: J. Rodellar

Copyright © 2010 Claudio Fernández et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study abstract equations of the form λu′′′(t)+u′′(t)=c2Au(t)+c2μAu(t)+f(t), 0<λ<μ which is motivated by the study of vibrations of flexible structures possessing internal material damping. We introduce the notion of (α;β;γ)-regularized families, which is a particular case of (a;k)-regularized families, and characterize maximal regularity in Lp-spaces based on the technique of Fourier multipliers. Finally, an application with the Dirichlet-Laplacian in a bounded smooth domain is given.