Completeness theorems on the boundary in thermoelasticity (Q2419330)

Let \(\Xi\) be the class of exponential polynomial solutions of the three-dimensional steady oscillation equation \[ \begin{cases} \mu \triangle u +(\lambda+\mu)\nabla \operatorname{div} U-\gamma \nabla U_4+\rho\omega^2 u=0 \\ \triangle U_4+ \frac{i\omega}{\kappa} U_4+i\omega\varrho \operatorname{div} U=0. \end{cases} \] Conditions on the parameter \(\omega^2\) are indicated, under which the class \(\Xi\) is complete in \(L^p(\partial\Omega)^4\), where \(\Omega\) is a bounded domain in \(\mathbb{R}^3\) with a Lyapunov boundary such that \(\mathbb{R}^3\setminus \Omega\) is connected. For the entire collection see [Zbl 1410.30002].