Energy quantization for Yamabe's problem in conformal dimension

Abstract

Rivière [11] proved an energy quantization for Yang-Mills fields defined on n-dimensional Riemannian manifolds, when n is larger than the critical dimension 4. More precisely, he proved that the defect measure of a weakly converging sequence of Yang-Mills fields is quantized, provided the W2,1 norm of their curvature is uniformly bounded. In the present paper, we prove a similar quantization phenomenon for the nonlinear elliptic equation -Δu = u|u|4/(n-2), in a subset Ω of ℝn.