SYMMETRY GROUPS AND PATH-INDEPENDENT INTEGRALS.

Noether's general theorem gives a one-to-one correspondence between nontrivial conservation laws or path independent integrals for the Euler-Lagrange equations of some variational problem and the generalized variational symmetries of the variational problem itself, provided that it satisfies certain nondegeneracy assumptions. Here we give a brief introduction to the theory of generalized symmetries and their connections with conservation laws. Applications are given to the classification of conservation laws for the equations of two dimensional elasticity, especially the linear isotropic and anisotropic cases.