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

• 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 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.
Mathematics Subject Classification: 35 .

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