We consider the linearized thermoelastic plate equation with the Dirichlet boundary condition in a general domain Ω, given by utt+Δ2u+normalΔθ=1ptf1,in3.0235ptnormalΩ×false(0,∞false),θt−normalΔθ−normalΔut=1ptf2,in3.0235ptnormalΩ×false(0,∞false), with the initial condition u|(t=0)=u0, ut|(t=0)=u1, and θ|(t=0)=θ0 in Ω and the boundary condition u=∂νu=θ=0 on Γ, where u=u(x,t) denotes a vertical displacement at time t at the point x=(x1,⋯,xn)∈Ω, while θ=θ(x,t) describes the temperature. This work extends the result obtained by Naito and Shibata that studied the problem in the half‐space case. We prove the existence of scriptR‐bounded solution operators of the corresponding resolvent problem. Then, the generation of C0 analytic semigroup and the maximal Lp‐Lq‐regularity of time‐dependent problem are derived.

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