Errata

Peter J. Olver
1988 Archive for Rational Mechanics and Analysis  
1. On page 133, formula (2.1) should be : = f{~z 11 89 (Vu + Vur)]l 2 + 89 u)2}dx, Q i.e. a factor of 89 was left out of the first term in the stored energy. 2. On page 134-135, and subsequently, there is an unfortunate error in the identification of the tensor S = ~ Vu + (~ + 4) (V. u) 1 (*) with the stress tensor a, whose correct expression is a = ~(Vu + Vu r) + ,t(V 9 u) 1. The confusion arises because both S and a determine the self-same system of Navier's equations: e[u] = V 9 s = V .a =
more » ... u + (~ + ~.) V(V 9 u) = 0. However, S and a are not the same tensor. They differ by a trivial conservation law z~a-S=/~(Vu r-(V'u) I), where "trivial" means that the divergence of z vanishes identically for all functions u(x): V "~0.
doi:10.1007/bf00251537 fatcat:7bwymxcgtnevloulae5kl5ufe4