Maximal Regularity for Flexible Structural Systems in Lebesgue Spaces

Abstract

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.