nergy quantization for Yamabe's problem in conformal dimension
Riviere [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 th...
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| Format: | Article |
| Language: | English |
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Texas State University
2006-07-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2006/71/abstr.html |
| Summary: | Riviere [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 $W^{2,1}$ norm of their curvature is uniformly bounded. In the present paper, we prove a similar quantization phenomenon for the nonlinear elliptic equation $$ - Delta{u}= u |u|^{4/(n-2)}, $$ in a subset $Omega$ of $mathbb{R}^n$. |
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| ISSN: | 1072-6691 |