Maximal regularity for the thermoelastic plate equations with free  boundary conditions

Denk, Robert; Shibata, Yoshihiro

Maximal regularity for the thermoelastic plate equations with free boundary conditions

Files

Denk_0-325845.pdf(557.55 KB)

Date

2016

Authors

Denk, Robert

Shibata, Yoshihiro

Series

Konstanzer Schriften in Mathematik; 352

Publication type

Working Paper/Technical Report

Publication status

Published

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 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.

Subject (DDC)

510 Mathematics

Keywords

Thermoelastic plate equations; generation of analytic semigroups; maximal Lp-Lq-regularity; R-bounded solution operator, operator-valued Fourier multipliers

Cite This

ISO 690

DENK, 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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