Maximal regularity for the thermoelastic plate equations with free boundary conditions

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2016
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Shibata, Yoshihiro
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Zusammenfassung

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.

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Fachgebiet (DDC)
510 Mathematik
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Thermoelastic plate equations; generation of analytic semigroups; maximal Lp-Lq-regularity; R-bounded solution operator, operator-valued Fourier multipliers
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ISO 690DENK, Robert, Yoshihiro SHIBATA, 2016. Maximal regularity for the thermoelastic plate equations with free boundary conditions
BibTex
@techreport{Denk2016Maxim-33539,
  year={2016},
  series={Konstanzer Schriften in Mathematik},
  title={Maximal regularity for the thermoelastic plate equations with free  boundary conditions},
  number={352},
  author={Denk, Robert and Shibata, Yoshihiro}
}
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    <dcterms:abstract xml:lang="eng">We consider the linear thermoelastic plate equations with free boundary conditions in the L&lt;sub&gt;p&lt;/sub&gt; in time and L&lt;sub&gt;q&lt;/sub&gt; in space setting. We obtain unique solvability with optimal regularity for the inhomogeneous problem in a uniform C&lt;sup&gt;4&lt;/sup&gt;-domain, which includes the cases of  a bounded domain and of an exterior domain with C&lt;sup&gt;4&lt;/sup&gt;-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.</dcterms:abstract>
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