Concentration-compactness principle and γ-convergence

Being given a sequence of open (or quasi-open) sets (A(n))(n is an element of N), with A(n) subset of or equal to R-n, not necessarily bounded, but of uniformly bounded measure, we prove a concentration-compactness result in L(L-2(R-N)) for the sequence of resolvent operators (R-An)(n is an element of N), where R-An : L-2(R-N) --> H-0(1)(A(n)), R-An = (-Delta)(-1). Making the connection with the gamma-convergence theory, we prove that the behavior in L-2(R-N) of an arbitrary sequence n bar right arrow u(n) is an element of H-0(1)(A(n)) is given by (R-An (1))(n). (C) Academie des Sciences/Elsevier, Paris