July  1999, 5(3): 585-598. doi: 10.3934/dcds.1999.5.585

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

1. 

Department of Mathematics, University of Virginia, Charlottesville, VA 22903

2. 

Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, VA 22904

Received  November 1998 Revised  February 1998 Published  May 1999

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.
Citation: Irena Lasiecka, Roberto Triggiani. A sharp trace result on a thermo-elastic plate equation with coupled hinged/Neumann boundary conditions. Discrete and Continuous Dynamical Systems, 1999, 5 (3) : 585-598. doi: 10.3934/dcds.1999.5.585
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