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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Dedicated to Jan Prüss on the occasion of his 65th birthday.
Partially supported by JSPS Grant-in-aid for Scientific Research (S) # 24224004 and Top Global University Project.
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Denk, R., Shibata, Y. Maximal regularity for the thermoelastic plate equations with free boundary conditions. J. Evol. Equ. 17, 215–261 (2017). https://doi.org/10.1007/s00028-016-0367-x
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DOI: https://doi.org/10.1007/s00028-016-0367-x