Abstract
We consider the linear thermoelastic plate equations with free boundary conditions in the $$L_p$$ in time and $$L_q$$ in space setting. We obtain unique solvability with optimal regularity for the inhomogeneous problem in a uniform $$C^4$$ -domain, which includes the cases of a bounded domain and of an exterior domain with $$C^4$$ -boundary. Moreover, we prove uniform a priori estimates for the solution. The proof is based on the existence of $${\mathcal R}$$ -bounded solution operators of the corresponding generalized resolvent problem which is shown with the help of an operator-valued Fourier multiplier theorem due to Weis.
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