This paper is devoted to the description of the lack of compactness of the
Sobolev embedding of H1(R2) in the critical Orlicz space {\cL}(\R^2). It
turns out that up to cores our result is expressed in terms of the
concentration-type examples derived by J. Moser in \cite{M} as in the radial
setting investigated in \cite{BMM}. However, the analysis we used in this work
is strikingly different from the one conducted in the radial case which is
based on an L∞ estimate far away from the origin and which is no
longer valid in the general framework. Within the general framework of
H1(R2), the strategy we adopted to build the profile decomposition in
terms of examples by Moser concentrated around cores is based on capacity
arguments and relies on an extraction process of mass concentrations. The
essential ingredient to extract cores consists in proving by contradiction that
if the mass responsible for the lack of compactness of the Sobolev embedding in
the Orlicz space is scattered, then the energy used would exceed that of the
starting sequence.Comment: Submitte