### Abstract

We consider the linear thermoelastic plate equations with free boundary conditions in the (Formula presented.) in time and (Formula presented.) in space setting. We obtain unique solvability with optimal regularity for the inhomogeneous problem in a uniform (Formula presented.)-domain, which includes the cases of a bounded domain and of an exterior domain with (Formula presented.)-boundary. Moreover, we prove uniform a priori estimates for the solution. The proof is based on the existence of (Formula presented.)-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.

Original language | English |
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Pages (from-to) | 1-47 |

Number of pages | 47 |

Journal | Journal of Evolution Equations |

DOIs | |

Publication status | Accepted/In press - 2016 Oct 28 |

### Keywords

- $${\mathcal R}$$R-Bounded solution operator
- Generation of analytic semigroups
- Maximal $$L_p$$Lp–$$L_q$$Lqregularity
- Operator-valued Fourier multipliers
- Thermoelastic plate equations

### ASJC Scopus subject areas

- Mathematics (miscellaneous)