  The present paper addresses the topic of boundary output feedback
stabilization of parabolic-type equations, governed by linear differential
operators which can be diagonalized by the introduction of adequate weighting
functions (by means of the Sturm-Liouville method), and which evolve in bounded
spatial domains that are subsets of $\mathbb{R}^d,\ d=1,2,3$.
  Combining ideas inspired by \cite{lhachemi2022finite} for the boundary output
feedback control of 1-D parabolic PDEs and \cite{munteanu2019boundary} for the
state feedback control of multi-D parabolic PDEs, we report in this paper an
output feedback boundary stabilizing control with internal Dirichlet
measurements designed by means of a finite-dimensional observer. The reported
control design procedure is shown to be systematic for 2-D and 3-D parabolic
equations.
