Well posedness for a class of flexible structure in Hölder spaces (Q1036332)

Summary: We characterize well-posedness in Hölder spaces for an abstract version of the equation \((\ast\;u''+\lambda u'''=c^2(\Delta u+\mu\Delta u')+f\) which model the vibrations of flexible structures possessing internal material damping and external force \(f\). As a consequence, we show that in case of the Laplacian with Dirichlet boundary conditions, equation \((\ast)\) is always well-posed provided \(0<\lambda<\mu\).