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

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

Symmetry analysis of the bidimensional Lane-Emden systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We carry out a complete group classification of the nonlinear Lane-Emden systems; in dimension two. The Noether symmetries are found and their corresponding conservation laws are established. (C) 2011 Elsevier Inc. All rights reserved.We carry out a complete group classification of the nonlinear Lane-Emden systems; in dimension two. The Noether symmetries are found and their corresponding conservation laws are established388212791284FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)SEM INFORMAÇÃOSEM INFORMAÇÃ

Mass and energy in general relativity

We consider the Denisov-Solov'ov example which shows that the inertial mass is not well defined in General Relativity. It is shown that the mathematical reason why this is true is a wrong application of the Stokes theorem. Then we discuss the role of the order of asymptotically flatness in the definition of the mass. In conclusion some comments on conservation laws in General Relativity are presented. © 1995 Plenum Publishing Corporation.We consider the Denisov-Solov'ov example which shows that the inertial mass is not well defined in General Relativity. It is shown that the mathematical reason why this is true is a wrong application of the Stokes theorem. Then we discuss the role of the278813819FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOSEM INFORMAÇÃOSEM INFORMAÇÃOWe would like to thank the referees for theirs suggestions and comments. Yu. Bozhkov would also like to thank FAPESP, S~o Paulo, Brasil, for the fellowship at State University of Campinas and the Commission of EC, "Diffusion Reaction Equations", grant No