Noether Symmetries and Critical Exponents

We show that all Lie point symmetries of various classes of nonlinear differential equations involving critical nonlinearities are variational/divergence symmetries.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

On the paper "Symmetry analysis of wave equation on sphere" by H. Azad and M. T. Mustafa

Using the scalar curvature of the product manifold S^{2}X R and the complete group classification of nonlinear Poisson equation on (pseudo) Riemannian manifolds, we extend the previous results on symmetry analysis of homogeneous wave equation obtained by H. Azad and M. T. Mustafa [H. Azad and M. T. Mustafa, Symmetry analysis of wave equation on sphere, J. Math. Anal. Appl., 333 (2007) 1180--1888] to nonlinear Klein-Gordon equations on the two-dimensional sphere.Comment: Version accepted in J. Math. Anal. App

Conservations Laws for Critical Kohn-Laplace Equations on the Heisenberg Group

Using the complete group classification of semilinear differential equations on the three-dimensional Heisenberg group carried out in a preceding work, we establish the conservation laws for the critical Kohn-Laplace equations via the Noether's Theorem.Comment: 9 pages, 1 table, submitted for publicatio

Special Conformal Groups of a Riemannian Manifold and Lie Point Symmetries of the Nonlinear Poisson Equation

We obtain a complete group classification of the Lie point symmetries of nonlinear Poisson equations on generic (pseudo) Riemannian manifolds M. Using this result we study their Noether symmetries and establish the respective conservation laws. It is shown that the projection of the Lie point symmetries on $M$ are special subgroups of the conformal group of M. In particular, if the scalar curvature of M vanishes, the projection on M of the Lie point symmetry group of the Poisson equation with critical nonlinearity is the conformal group of the manifold. We illustrate our results by applying them to the Thurston geometries.Comment: Paper submitted for publicatio

Pohozhaev and Morawetz Identities in Elastostatics and Elastodynamics

We construct identities of Pohozhaev type, in the context of elastostatics and elastodynamics, by using the Noetherian approach. As an application, a non-existence result for forced semi-linear isotropic and anisotropic elastic systems is established