35 research outputs found
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 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