Concentration-compactness principle and extremal functions for a sharp Trudinger-Moser inequality

摘要

We prove a concentration-compactness principle for the Trudinger-Moser functional associated with a class of weighted Sobolev spaces including fractional dimensions. Based in this result and using blow up analysis we establish a sharp form of Trudinger-Moser type inequality for this class of weighted Sobolev spaces. Moreover, we discuss the existence of extremal for the maximizing problem associated with this new Trudinger-Moser inequality.