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.
Concentration-compactness principles for Moser-Trudinger inequalities: new results and proofs / Robert Cerny; Andrea Cianchi; Stanislav Hencl. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 192:(2013), pp. 225-243.
Concentration-compactness principles for Moser-Trudinger inequalities: new results and proofs
CIANCHI, ANDREA;
2013
Abstract
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.File | Dimensione | Formato | |
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