Energy quantization for Yamabe's problem in conformal dimension
Date
2006-07-07
Authors
Mahmoudi, Fethi
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
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.
Description
Keywords
Critical exponents, Lorentz spaces, Quantization phenomena
Citation
Mahmoudi, F. (2006). Energy quantization for Yamabe's problem in conformal dimension. <i>Electronic Journal of Differential Equations, 2006</i>(71), pp. 1-17.
Rights
Attribution 4.0 International