Abstract
We consider here the Dirichlet's problem for the Lame's equations without body force in a semi-infinite cylinder (0≤z<∞) with cross-sectionS z , the displacementsu i vanishing on the cylindrical surface. We give in this paper an explicit decay estimate for aL 2-norm ofu i . The evaluation is of the type $$k_1 (\alpha )I(f_i )e^{ - k_2 (\alpha ,\lambda )z} $$ wherek 1 andk 2 are determined constants andI(f i ) an integral depending only on the displacementsf i prescribed onS 0. Our results consequently reinforce the Saint-Venant's principle.
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