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Description:
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 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. ; published