A sharp trace result on a thermo-elastic plate equation with coupled hinged/Neumann boundary conditions

Abstract

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 '$\frac{1}{2}$' 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 byenergy methods are given: one which reduces the analysis to sharp wave equation'sregularity theory; and one which analyzes directly the corresponding Kirchoff elasticequation. Important implications of this result are noted.