Maximal regularity for the thermoelastic plate equations with free boundary conditions

Robert Denk; Yoshihiro Shibata

doi:10.1007/s00028-016-0367-x

Maximal regularity for the thermoelastic plate equations with free boundary conditions

Robert Denk^*, Yoshihiro Shibata

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	215-261
Number of pages	47
Journal	Journal of Evolution Equations
Volume	17
Issue number	1
DOIs	https://doi.org/10.1007/s00028-016-0367-x
Publication status	Published - 2017 Mar 1

Keywords

Generation of analytic semigroups
Maximal L–L regularity
Operator-valued Fourier multipliers
R-Bounded solution operator
Thermoelastic plate equations

ASJC Scopus subject areas

Mathematics (miscellaneous)

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title = "Maximal regularity for the thermoelastic plate equations with free boundary conditions",

abstract = "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.",

keywords = "Generation of analytic semigroups, Maximal L–L regularity, Operator-valued Fourier multipliers, R-Bounded solution operator, Thermoelastic plate equations",

author = "Robert Denk and Yoshihiro Shibata",

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doi = "10.1007/s00028-016-0367-x",

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T1 - Maximal regularity for the thermoelastic plate equations with free boundary conditions

AU - Denk, Robert

AU - Shibata, Yoshihiro

PY - 2017/3/1

Y1 - 2017/3/1

N2 - 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.

AB - 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.

KW - Generation of analytic semigroups

KW - Maximal L–L regularity

KW - Operator-valued Fourier multipliers

KW - R-Bounded solution operator

KW - Thermoelastic plate equations

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JO - Journal of Evolution Equations

JF - Journal of Evolution Equations

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Maximal regularity for the thermoelastic plate equations with free boundary conditions

Abstract

Keywords

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