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 languageEnglish
    Pages (from-to)1-47
    Number of pages47
    JournalJournal of Evolution Equations
    DOIs
    Publication statusAccepted/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

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

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

    Research output: Contribution to journalArticle

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    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.",
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