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, in large dimensions, 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.
Bruno Premoselli (Bruxelles): Existence of infinitely many solutions for the Einstein‐Lichnerowicz system
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