Abstract Concentration Compactness and Elliptic Equations on Unbounded Domains
Ian Schindler, Kyril Tintarev · Birkhäuser Boston eBooks · 2001
The notion of concentration compactness, used in numerous applications (cf. P.-L.Lions [4],[5]), was formulated originally in terms of specific functional spaces. In fact, much of the method can be formulated in general terms of a non-compact groupGof bounded operators on a Banach spaceE.We say that a bounded sequence Uk converges to zeroweakly with concentrationif for any sequencegk∈G gkuk converges weakly to zero. IfGis a compact group, the concentrated weak convergence is equivalent to the weak convergence.