Energy Quantization for Yamabe's problem in Conformal Dimension

Details Energy Quantization for Yamabe's problem in Conformal Dimension Energy Quantization for Yamabe's problem in Conformal Dimension

2006-09-04

arxiv.org/abs/math/0609103v1

Electron. J. Diff. Eqns., Vol. 2006(2006), No. 71, pp. 1-17

Mathematics

Analysis of PDEs

16 pages

Scientific paper

T. Riviere 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 $W^{2,1}$ norm of their curvature is uniformly bounded. In the present paper, we prove a similar quantization phenomenon for the Yamabe problem in a bounded domain $\Omega$ of $R^n$.

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