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

Abstrakt

We are concerned with the best exponent in Concentration-Compactness estimates for the borderline case of the Sobolev inequality. We present a new approach, which yields a rigorous proof of the relevant estimate in the standard case when functions vanishing on the boundary are considered, and,importantly, enables us to deal with functions with unrestricted boundary values.

Klíčová slova

• concentration
• compactness