Concentration-compactness principle of singular Trudinger-Moser inequality involving N-Finsler-Laplacian operator

In this paper, suppose F : RN -> [0, + infinity) be a convex function of class C-2 (R-N\{0}) which is even and positively homogeneous of degree 1. We establish the Lions type concentration-compactness principle of singular Trudinger-Moser Inequalities involving N-Finsler-Laplacian operator. Let Omega subset of R-N (N >= 2) be a smooth bounded domain. {u(n)} subset of W-0(1,N) (Omega) be a sequence such that anisotropic Dirichlet norm integral(Omega) F-N (del u(n))dx = 1, u(n) -> u not equivalent to 0 weakly in W-0(1,N) (Omega). Denote 0 < p < p(N )(u) = {(1 - integral(Omega) F-N (del u)dx)(-1/N-1), if integral(Omega) F-N(del u) < 1, infinity, if integral(Omega) F-N(del u) = 1, Then we have integral(Omega) e(lambda N(1-beta/N)p vertical bar un vertical bar N/N-1)/F-o(x)(beta)dx < + infinity, where 0 <= beta < N, lambda(N) = NN/N-1 kappa(1/N-1)(N) is and kappa(N) is the volume of a unit Wulff ball. This conclusion fails if p >= p(N)(u). Furthermore, we also obtain the corresponding concentration-compactness principle in the entire Euclidean space R-N.