Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 71, pp. 1-17.
Title: Energy quantization for Yamabe's problem in conformal dimension
Author: Fethi Mahmoudi (Scuola Intl. Superiore, Trieste, Italy)
Abstract:
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 $\mathbb{R}^n$.
Submitted February 20, 2006. Published July 7, 2006.
Math Subject Classifications: 35B33, 46E30, 46L65.
Key Words: Critical exponents; Lorentz spaces; quantization phenomena.