American Institute of Mathematical Sciences

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 & Continuous Dynamical Systems - A, 1999, 5 (3) : 585-598. doi: 10.3934/dcds.1999.5.585
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