### Abstract

We consider the linear thermoelastic plate equations with free boundary conditions in the (Formula presented.) in time and (Formula presented.) in space setting. We obtain unique solvability with optimal regularity for the inhomogeneous problem in a uniform (Formula presented.)-domain, which includes the cases of a bounded domain and of an exterior domain with (Formula presented.)-boundary. Moreover, we prove uniform a priori estimates for the solution. The proof is based on the existence of (Formula presented.)-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) | 1-47 |

Number of pages | 47 |

Journal | Journal of Evolution Equations |

DOIs | |

Publication status | Accepted/In press - 2016 Oct 28 |

### Fingerprint

### Keywords

- $${\mathcal R}$$R-Bounded solution operator
- Generation of analytic semigroups
- Maximal $$L_p$$Lp–$$L_q$$Lqregularity
- Operator-valued Fourier multipliers
- Thermoelastic plate equations

### ASJC Scopus subject areas

- Mathematics (miscellaneous)

### Cite this

**Maximal regularity for the thermoelastic plate equations with free boundary conditions.** / Denk, Robert; Shibata, Yoshihiro.

Research output: Contribution to journal › Article

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TY - JOUR

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

AU - Denk, Robert

AU - Shibata, Yoshihiro

PY - 2016/10/28

Y1 - 2016/10/28

N2 - We consider the linear thermoelastic plate equations with free boundary conditions in the (Formula presented.) in time and (Formula presented.) in space setting. We obtain unique solvability with optimal regularity for the inhomogeneous problem in a uniform (Formula presented.)-domain, which includes the cases of a bounded domain and of an exterior domain with (Formula presented.)-boundary. Moreover, we prove uniform a priori estimates for the solution. The proof is based on the existence of (Formula presented.)-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 (Formula presented.) in time and (Formula presented.) in space setting. We obtain unique solvability with optimal regularity for the inhomogeneous problem in a uniform (Formula presented.)-domain, which includes the cases of a bounded domain and of an exterior domain with (Formula presented.)-boundary. Moreover, we prove uniform a priori estimates for the solution. The proof is based on the existence of (Formula presented.)-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 - $${\mathcal R}$$R-Bounded solution operator

KW - Generation of analytic semigroups

KW - Maximal $$L_p$$Lp–$$L_q$$Lqregularity

KW - Operator-valued Fourier multipliers

KW - Thermoelastic plate equations

UR - http://www.scopus.com/inward/record.url?scp=84992735877&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84992735877&partnerID=8YFLogxK

U2 - 10.1007/s00028-016-0367-x

DO - 10.1007/s00028-016-0367-x

M3 - Article

SP - 1

EP - 47

JO - Journal of Evolution Equations

JF - Journal of Evolution Equations

SN - 1424-3199

ER -