Abstract:

This talk is about the evolution problem associated to the Einstein-Vlasov equations, with initial data specified on two transversally intersecting characteristic hypersurfaces. The main existence and uniqueness result of the work is obtained by a contracting mapping principle, combined with Sobolev inequalities and Moser estimates as well as energy inequalities for first order and second order linear hyperbolic equations. The whole investigation is conducted in appropriate weighted Sobolev spaces.