Data di Pubblicazione:
2013
Citazione:
Optimal Sobolev Type Inequalities in Lorentz Spaces / D. Cassani, B. Ruf, C. Tarsi. - In: POTENTIAL ANALYSIS. - ISSN 0926-2601. - 39:3(2013 Oct), pp. 265-285.
Abstract:
It is well known that the classical Sobolev embeddings may be improved within the framework of Lorentz spaces L p,q : the space D 1,p (R n ) , 1 < p < n, embeds into L p ∗ ,q (R n ) , p ≤ q ≤ ∞. However, the value of the best possible embedding constants in the corresponding inequalities is known just in the case L p ∗ ,p (R n ) . Here, we determine optimal constants for the embedding of the space D 1,p (R n ) , 1 < p < n, into the whole Lorentz space scale L p ∗ ,q (R n ) , p ≤ q ≤ ∞, including the limiting case q = p of which we give a new proof. We also exhibit extremal functions for these embedding inequalities by solving related elliptic problems.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Best constants; Critical growth; Elliptic equations; Lorentz spaces; Optimal embeddings; Sobolev inequalities
Elenco autori:
D. Cassani, B. Ruf, C. Tarsi
Link alla scheda completa: