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Maximal regularity for the thermoelastic plate equations with free boundary conditions

Maximal regularity for the thermoelastic plate equations with free boundary conditions

Type of Publication: Working Paper/Technical Report
Publication status: Published
URI (citable link): http://nbn-resolving.de/urn:nbn:de:bsz:352-0-325845
Author: Denk, Robert; Shibata, Yoshihiro
Year of publication: 2016
Series: Konstanzer Schriften in Mathematik ; 352
Summary:
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.
MSC Classification: 35K35; 35J40; 42B15
Subject (DDC): 510 Mathematics
Keywords: Thermoelastic plate equations; generation of analytic semigroups; maximal Lp-Lq-regularity; R-bounded solution operator, operator-valued Fourier multipliers
Link to License: In Copyright
Bibliography of Konstanz: Yes

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DENK, Robert, Yoshihiro SHIBATA, 2016. Maximal regularity for the thermoelastic plate equations with free boundary conditions

@techreport{Denk2016Maxim-33539, series={Konstanzer Schriften in Mathematik}, title={Maximal regularity for the thermoelastic plate equations with free boundary conditions}, year={2016}, number={352}, author={Denk, Robert and Shibata, Yoshihiro} }

terms-of-use eng We consider the linear thermoelastic plate equations with free boundary conditions in the L<sub>p</sub> in time and L<sub>q</sub> in space setting. We obtain unique solvability with optimal regularity for the inhomogeneous problem in a uniform C<sup>4</sup>-domain, which includes the cases of a bounded domain and of an exterior domain with C<sup>4</sup>-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. Shibata, Yoshihiro Denk, Robert 2016-04-01T11:18:27Z Denk, Robert Shibata, Yoshihiro 2016 Maximal regularity for the thermoelastic plate equations with free boundary conditions 2016-04-01T11:18:27Z

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