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Geometric Analysis and Partial Differential Equations Seminar
September 3, 2013 @ 10:30 am - 11:30 pm
Prof. Jerome Vetois (Nice Sophia Antipolis University)
Instability of the Yamabe Equation under linear perturbations of the potential
In this talk, I will present a joint work with P. Esposito and A. Pistoia on the instability of the set of solutions of the Yamabe Equation. We prove that a linear perturbation of the potential can generate the existence of blowing-up families of solutions. I will also present a joint work with F. Robert on the existence of blowing-up families of solutions which admit a non-isolated blow-up point. These results complete previous stability results and allow to have a sharp picture of the stability/instability of scalar curvature type equations on compact manifolds.