A sharp trace result on a thermo-elastic plate equation with coupled hinged/Neumann boundary conditions
In this paper we consider a thermo-elastic plate equation with rotational forces [Lagnese.1] and with coupled hinged mechanical/Neumann thermal boundary conditions (B.C.). We give a sharp result on the Neumann trace of the mechanical velocity, which is "1/2" sharper in the space variable than the result than one would obtain by a formal application of trace theory on the optimal interior regularity. Two proofs by energy methods are given: one which reduces the analysis to sharp wave equation's regularity theory; and one which analyzes directly the corresponding Kirchoff elastic equation. Important implications of this result are noted.
Discrete and Continuous Dynamical Systems
Lasiecka, I., & Triggiani, R. (1999). A sharp trace result on a thermo-elastic plate equation with coupled hinged/Neumann boundary conditions. Discrete and Continuous Dynamical Systems, 5 (3), 585-598. https://doi.org/10.3934/dcds.1999.5.585