Fine multibubble analysis in the higher-dimensional Brezis-Nirenberg problem

For a bounded set Omega subset of R-N and a perturbation V is an element of C-1((Omega) over bar), we analyze the concentration behavior of a blow-up sequence of positive solutions to -Delta u(epsilon)+epsilon Vu(epsilon)=N(N-2)u epsilon((N-2)(N+2)) for dimensions N >= 4, which are non-critical in the sense of the Brezis-Nirenberg problem. For the general case of multiple concentration points, we prove that concentration points are isolated and characterize the vector of these points as a critical point of a suitable function derived from the Green function of -Delta on Omega. Moreover, we give the leading-order expression of the concentration speed. This paper, with a recent one by the authors [arXiv:2208.12337, 2022] in dimension N = 3, gives a complete picture of blow-up phenomena in the Brezis-Nirenberg framework.