Concentration-compactness principles for Moser-Trudinger inequalities: new results and proofs

We are concerned with the best exponent in Concentration-Compactness principles for the borderline case of the Sobolev inequality. We present a new approach, which both yields a rigorous proof of the relevant principle in the standard case when functions vanishing on the boundary are considered, and enables us to deal with functions with unrestricted boundary values. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM.