The constraint equations arise in the initial-value formulation of the Einstein equations. The conformal method allows one to rewrite the constraint equations into a determined system of nonlinear, supercritical, elliptic PDEs.

We will investigate in this talk stability properties for this elliptic system. The notion of stability considered here, defined as the continuous dependence of the set of solutions of the conformal constraint system in its coefficients, reformulates in terms of the relevance of the conformal method. The analysis of the aforementioned stability properties involves blow-up techniques for the analysis of defects of compactness of supercritical nonlinear elliptic equations.

Joint work with Olivier Druet.