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

Irena Lasiecka; Roberto Triggiani

doi:10.3934/dcds.1999.5.585

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1999, Volume 5, Issue 3: 585-598. Doi: 10.3934/dcds.1999.5.585

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

Irena Lasiecka^1, and
Roberto Triggiani^2,

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: October 31, 1998

Revised: January 31, 1998

Published: June 1999

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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 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.

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Mathematics Subject Classification: 35 .

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