# Maximal regularity for the thermoelastic plate equations with free boundary conditions

Robert Denk, Yoshihiro Shibata

Research output: Contribution to journalArticle

5 Citations (Scopus)

### 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 1-47 47 Journal of Evolution Equations https://doi.org/10.1007/s00028-016-0367-x Accepted/In press - 2016 Oct 28

### Fingerprint

Plate Equation
Maximal Regularity
Thermoelastic
Free Boundary
Boundary conditions
Operator-valued Fourier multipliers
Unique Solvability
Uniform Estimates
Exterior Domain
Bounded Solutions
A Priori Estimates
Resolvent
Bounded Domain
Regularity
Operator
Theorem

### 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

In: Journal of Evolution Equations, 28.10.2016, p. 1-47.

Research output: Contribution to journalArticle

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