Uniqueness and continuous data dependence in the elastic cylinder

Abstract

Selected continuous data dependence is established for the linearised elastic cylinder under relaxed positive-definite and homogeneity conditions on elasticities in the superposed linear deformation and for constrained sets of the solution. The proofs are based on those in [Math. Proc. Cambridge Philos. Soc. 103 (1988) 535] and employ a Lagrange identity obtained from Betti's reciprocal theorem. The treatment is intended only to be indicative of the method and is restricted to dependence on body force, certain base data, and the superposed elasticities in the half-length of the finite cylinder. Estimates are also presented for the semi-infinite cylinder under alternative boundary conditions. Uniqueness of the solution is also established.