We consider the linear thermoelastic plate equations with free boundary conditions in the Lp in time and Lq in space setting. We obtain unique solvability with optimal regularity for the inhomogeneous problem in a uniform C4-domain, which includes the cases of a bounded domain and of an exterior domain with C4-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.
- Generation of analytic semigroups
- Maximal L–L regularity
- Operator-valued Fourier multipliers
- R-Bounded solution operator
- Thermoelastic plate equations
ASJC Scopus subject areas
- Mathematics (miscellaneous)