Bruno Premoselli (ULB, Brussels)
Title: Existence of infinitely many solutions for the Einstein-Lichnerowicz system
Abstract: We will consider in this talk the Einstein-Lichnerowicz system of equations. It originates in General Relativity as a way to determine initial-data sets for the evolution problem. This system takes the form of a strongly coupled, supercritical, nonlinear system of elliptic PDEs. We will investigate its blow-up properties and show that, under some assumptions on the physics data, it possesses a non-compact family of solutions. This family of solutions will be constructed by combining toplogical methods with a finite-dimensional reduction approach; due to the non-variational structure of the system, the latter has to be carried on in strong spaces and relies of a priori blow-up estimates that we shall describe.